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Angular momentum is an extensive quantity; that is, the total angular momentum of any composite system is the sum of the angular momenta of its constituent parts. For a continuous rigid body or a fluid, the total angular momentum is the volume integral of angular momentum density (angular momentum per unit volume in the limit as volume shrinks to zero) over the entire body.
Similar to conservation of linear momentum, where it is conserved if there is no external force, angular momentum is conserved if there is no external torque. Torque can be defined as the rate of change of angular momentum, analogous to force. The net "external" torque on any system is always equal to the "total" torque on the system; the sum of all internal torques of any system is always 0 (this is the rotational analogue of Newton's third law of motion). Therefore, for a closed system (where there is no net external torque), the "total" torque on the system must be 0, which means that the total angular momentum of the system is constant.
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The change in angular momentum for a particular interaction is called angular impulse, sometimes twirl. Angular impulse is the angular analog of (linear) impulse.
Examples.
The trivial case of the angular momentum formula_1 of a body in an orbit is given by
formula_2
where formula_3 is the mass of the orbiting object, formula_4 is the orbit's frequency and formula_5 is the orbit's radius.
The angular momentum formula_1 of a uniform rigid sphere rotating around its axis, instead, is given by
formula_7
where formula_3 is the sphere's mass, formula_4 is the frequency of rotation and formula_5 is the sphere's radius.
Thus, for example, the orbital angular momentum of the Earth with respect to the Sun is about 2.66 × 1040 kg⋅m2⋅s−1, while its rotational angular momentum is about 7.05 × 1033 kg⋅m2⋅s−1.
In the case of a uniform rigid sphere rotating around its axis, if, instead of its mass, its density is known, the angular momentum formula_1 is given by
formula_12
where formula_13 is the sphere's density, formula_4 is the frequency of rotation and formula_5 is the sphere's radius.
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In the simplest case of a spinning disk, the angular momentum formula_1 is given by
formula_17
where formula_3 is the disk's mass, formula_4 is the frequency of rotation and formula_5 is the disk's radius.
If instead the disk rotates about its diameter (e.g. coin toss), its angular momentum formula_1 is given by
formula_22
Definition in classical mechanics.
Just as for angular velocity, there are two special types of angular momentum of an object: the spin angular momentum is the angular momentum about the object's center of mass, while the orbital angular momentum is the angular momentum about a chosen center of rotation. The Earth has an orbital angular momentum by nature of revolving around the Sun, and a spin angular momentum by nature of its daily rotation around the polar axis. The total angular momentum is the sum of the spin and orbital angular momenta. In the case of the Earth the primary conserved quantity is the total angular momentum of the Solar System because angular momentum is exchanged to a small but important extent among the planets and the Sun. The orbital angular momentum vector of a point particle is always parallel and directly proportional to its orbital angular velocity vector ω, where the constant of proportionality depends on both the mass of the particle and its distance from origin. The spin angular momentum vector of a rigid body is proportional but not always parallel to the spin angular velocity vector Ω, making the constant of proportionality a second-rank tensor rather than a scalar.
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Orbital angular momentum in two dimensions.
Angular momentum is a vector quantity (more precisely, a pseudovector) that represents the product of a body's rotational inertia and rotational velocity (in radians/sec) about a particular axis. However, if the particle's trajectory lies in a single plane, it is sufficient to discard the vector nature of angular momentum, and treat it as a scalar (more precisely, a pseudoscalar). Angular momentum can be considered a rotational analog of linear momentum. Thus, where linear momentum is proportional to mass and linear speed
formula_23
angular momentum is proportional to moment of inertia and angular speed measured in radians per second.
formula_24
Unlike mass, which depends only on amount of matter, moment of inertia depends also on the position of the axis of rotation and the distribution of the matter. Unlike linear velocity, which does not depend upon the choice of origin, orbital angular velocity is always measured with respect to a fixed origin. Therefore, strictly speaking, should be referred to as the angular momentum "relative to that center".
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In the case of circular motion of a single particle, we can use formula_25 and formula_26 to expand angular momentum as formula_27 reducing to:
formula_28
the product of the radius of rotation and the linear momentum of the particle formula_29, where formula_30 is the linear (tangential) speed.
This simple analysis can also apply to non-circular motion if one uses the component of the motion perpendicular to the radius vector:
formula_31
where formula_32 is the perpendicular component of the motion. Expanding, formula_33 rearranging, formula_34 and reducing, angular momentum can also be expressed,
formula_35
where formula_36 is the length of the "moment arm", a line dropped perpendicularly from the origin onto the path of the particle. It is this definition, , to which the term "moment of momentum" refers.
Scalar angular momentum from Lagrangian mechanics.
Another approach is to define angular momentum as the conjugate momentum (also called canonical momentum) of the angular coordinate formula_37 expressed in the Lagrangian of the mechanical system. Consider a mechanical system with a mass formula_38 constrained to move in a circle of radius formula_5 in the absence of any external force field. The kinetic energy of the system is
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formula_40
And the potential energy is
formula_41
Then the Lagrangian is
formula_42
The "generalized momentum" "canonically conjugate to" the coordinate formula_37 is defined by
formula_44
Orbital angular momentum in three dimensions.
To completely define orbital angular momentum in three dimensions, it is required to know the rate at which the position vector sweeps out an angle, the direction perpendicular to the instantaneous plane of angular displacement, and the mass involved, as well as how this mass is distributed in space. By retaining this vector nature of angular momentum, the general nature of the equations is also retained, and can describe any sort of three-dimensional motion about the center of rotation – circular, linear, or otherwise. In vector notation, the orbital angular momentum of a point particle in motion about the origin can be expressed as:
formula_45
where
This can be expanded, reduced, and by the rules of vector algebra, rearranged:
formula_52
which is the cross product of the position vector formula_48 and the linear momentum formula_54 of the particle. By the definition of the cross product, the formula_55 vector is perpendicular to both formula_48 and formula_57. It is directed perpendicular to the plane of angular displacement, as indicated by the right-hand rule – so that the angular velocity is seen as counter-clockwise from the head of the vector. Conversely, the formula_55 vector defines the plane in which formula_48 and formula_57 lie.
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By defining a unit vector formula_61 perpendicular to the plane of angular displacement, a scalar angular speed formula_62 results, where
formula_63 and
formula_64 where formula_65 is the perpendicular component of the motion, as above.
The two-dimensional scalar equations of the previous section can thus be given direction:
formula_66
and formula_67 for circular motion, where all of the motion is perpendicular to the radius formula_5.
In the spherical coordinate system the angular momentum vector expresses as
Analogy to linear momentum.
Angular momentum can be described as the rotational analog of linear momentum. Like linear momentum it involves elements of mass and displacement. Unlike linear momentum it also involves elements of position and shape.
Many problems in physics involve matter in motion about some certain point in space, be it in actual rotation about it, or simply moving past it, where it is desired to know what effect the moving matter has on the point—can it exert energy upon it or perform work about it? Energy, the ability to do work, can be stored in matter by setting it in motion—a combination of its inertia and its displacement. Inertia is measured by its mass, and displacement by its velocity. Their product,
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formula_70
is the matter's momentum. Referring this momentum to a central point introduces a complication: the momentum is not applied to the point directly. For instance, a particle of matter at the outer edge of a wheel is, in effect, at the end of a lever of the same length as the wheel's radius, its momentum turning the lever about the center point. This imaginary lever is known as the "moment arm". It has the effect of multiplying the momentum's effort in proportion to its length, an effect known as a "moment". Hence, the particle's momentum referred to a particular point,
formula_71
is the "angular momentum", sometimes called, as here, the "moment of momentum" of the particle versus that particular center point. The equation formula_72 combines a moment (a mass formula_38 turning moment arm formula_5) with a linear (straight-line equivalent) speed formula_75. Linear speed referred to the central point is simply the product of the distance formula_5 and the angular speed formula_62 versus the point: formula_78 another moment. Hence, angular momentum contains a double moment: formula_79 Simplifying slightly, formula_80 the quantity formula_81 is the particle's moment of inertia, sometimes called the second moment of mass. It is a measure of rotational inertia.
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The above analogy of the translational momentum and rotational momentum can be expressed in vector form:
The direction of momentum is related to the direction of the velocity for linear movement. The direction of angular momentum is related to the angular velocity of the rotation.
Because moment of inertia is a crucial part of the spin angular momentum, the latter necessarily includes all of the complications of the former, which is calculated by multiplying elementary bits of the mass by the squares of their distances from the center of rotation. Therefore, the total moment of inertia, and
the angular momentum, is a complex function of the configuration of the matter about the center of rotation and the orientation of the rotation for the various bits.
For a rigid body, for instance a wheel or an asteroid, the orientation of rotation is simply the position of the rotation axis versus the matter of the body. It may or may not pass through the center of mass, or it may lie completely outside of the body. For the same body, angular momentum may take a different value for every possible axis about which rotation may take place. It reaches a minimum when the axis passes through the center of mass.
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For a collection of objects revolving about a center, for instance all of the bodies of the Solar System, the orientations may be somewhat organized, as is the Solar System, with most of the bodies' axes lying close to the system's axis. Their orientations may also be completely random.
In brief, the more mass and the farther it is from the center of rotation (the longer the moment arm), the greater the moment of inertia, and therefore the greater the angular momentum for a given angular velocity. In many cases the moment of inertia, and hence the angular momentum, can be simplified by,
formula_84where formula_85 is the radius of gyration, the distance from the axis at which the entire mass formula_38 may be considered as concentrated.
Similarly, for a point mass formula_38 the moment of inertia is defined as,
formula_88where formula_5 is the radius of the point mass from the center of rotation, and for any collection of particles formula_90 as the sum,
formula_91
Angular momentum's dependence on position and shape is reflected in its units versus linear momentum: kg⋅m2/s or N⋅m⋅s for angular momentum versus kg⋅m/s or N⋅s for linear momentum. When calculating angular momentum as the product of the moment of inertia times the angular velocity, the angular velocity must be expressed in radians per second, where the radian assumes the dimensionless value of unity. (When performing dimensional analysis, it may be productive to use which treats radians as a base unit, but this is not done in the International system of units). The units if angular momentum can be interpreted as torque⋅time. An object with angular momentum of can be reduced to zero angular velocity by an angular impulse of .
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The plane perpendicular to the axis of angular momentum and passing through the center of mass is sometimes called the "invariable plane", because the direction of the axis remains fixed if only the interactions of the bodies within the system, free from outside influences, are considered. One such plane is the invariable plane of the Solar System.
Angular momentum and torque.
Newton's second law of motion can be expressed mathematically,
formula_92
or force = mass × acceleration. The rotational equivalent for point particles may be derived as follows:
formula_93
which means that the torque (i.e. the time derivative of the angular momentum) is
formula_94
Because the moment of inertia is formula_95, it follows that formula_96, and formula_97 which, reduces to
formula_98
This is the rotational analog of Newton's second law. Note that the torque is not necessarily proportional or parallel to the angular acceleration (as one might expect). The reason for this is that the moment of inertia of a particle can change with time, something that cannot occur for ordinary mass.
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Conservation of angular momentum.
General considerations.
A rotational analog of Newton's third law of motion might be written, "In a closed system, no torque can be exerted on any matter without the exertion on some other matter of an equal and opposite torque about the same axis." Hence, "angular momentum can be exchanged between objects in a closed system, but total angular momentum before and after an exchange remains constant (is conserved)".
Seen another way, a rotational analogue of Newton's first law of motion might be written, "A rigid body continues in a state of uniform rotation unless acted upon by an external influence." Thus "with no external influence to act upon it, the original angular momentum of the system remains constant".
The conservation of angular momentum is used in analyzing "central force motion". If the net force on some body is directed always toward some point, the "center", then there is no torque on the body with respect to the center, as all of the force is directed along the radius vector, and none is perpendicular to the radius. Mathematically, torque formula_99 because in this case formula_48 and formula_101 are parallel vectors. Therefore, the angular momentum of the body about the center is constant. This is the case with gravitational attraction in the orbits of planets and satellites, where the gravitational force is always directed toward the primary body and orbiting bodies conserve angular momentum by exchanging distance and velocity as they move about the primary. Central force motion is also used in the analysis of the Bohr model of the atom.
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For a planet, angular momentum is distributed between the spin of the planet and its revolution in its orbit, and these are often exchanged by various mechanisms. The conservation of angular momentum in the Earth–Moon system results in the transfer of angular momentum from Earth to Moon, due to tidal torque the Moon exerts on the Earth. This in turn results in the slowing down of the rotation rate of Earth, at about 65.7 nanoseconds per day, and in gradual increase of the radius of Moon's orbit, at about 3.82 centimeters per year.
The conservation of angular momentum explains the angular acceleration of an ice skater as they bring their arms and legs close to the vertical axis of rotation. By bringing part of the mass of their body closer to the axis, they decrease their body's moment of inertia. Because angular momentum is the product of moment of inertia and angular velocity, if the angular momentum remains constant (is conserved), then the angular velocity (rotational speed) of the skater must increase.
The same phenomenon results in extremely fast spin of compact stars (like white dwarfs, neutron stars and black holes) when they are formed out of much larger and slower rotating stars.
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Conservation is not always a full explanation for the dynamics of a system but is a key constraint. For example, a spinning top is subject to gravitational torque making it lean over and change the angular momentum about the nutation axis, but neglecting friction at the point of spinning contact, it has a conserved angular momentum about its spinning axis, and another about its precession axis. Also, in any planetary system, the planets, star(s), comets, and asteroids can all move in numerous complicated ways, but only so that the angular momentum of the system is conserved.
Noether's theorem states that every conservation law is associated with a symmetry (invariant) of the underlying physics. The symmetry associated with conservation of angular momentum is rotational invariance. The fact that the physics of a system is unchanged if it is rotated by any angle about an axis implies that angular momentum is conserved.
Relation to Newton's second law of motion.
While angular momentum total conservation can be understood separately from Newton's laws of motion as stemming from Noether's theorem in systems symmetric under rotations, it can also be understood simply as an efficient method of calculation of results that can also be otherwise arrived at directly from Newton's second law, together with laws governing the forces of nature (such as Newton's third law, Maxwell's equations and Lorentz force). Indeed, given initial conditions of position and velocity for every point, and the forces at such a condition, one may use Newton's second law to calculate the second derivative of position, and solving for this gives full information on the development of the physical system with time. Note, however, that this is no longer true in quantum mechanics, due to the existence of particle spin, which is youssef elfarouk momentum that cannot be described by the cumulative effect of point-like motions in space.
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As an example, consider decreasing of the moment of inertia, e.g. when a figure skater is pulling in their hands, speeding up the circular motion. In terms of angular momentum conservation, we have, for angular momentum "L", moment of inertia "I" and angular velocity "ω":
formula_102
Using this, we see that the change requires an energy of:
formula_103
so that a decrease in the moment of inertia requires investing energy.
This can be compared to the work done as calculated using Newton's laws. Each point in the rotating body is accelerating, at each point of time, with radial acceleration of:
formula_104
Let us observe a point of mass "m", whose position vector relative to the center of motion is perpendicular to the z-axis at a given point of time, and is at a distance "z". The centripetal force on this point, keeping the circular motion, is:
formula_105
Thus the work required for moving this point to a distance "dz" farther from the center of motion is:
formula_106
For a non-pointlike body one must integrate over this, with "m" replaced by the mass density per unit "z". This gives:
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formula_107
which is exactly the energy required for keeping the angular momentum conserved.
Note, that the above calculation can also be performed per mass, using kinematics only. Thus the phenomena of figure skater accelerating tangential velocity while pulling their hands in, can be understood as follows in layman's language: The skater's palms are not moving in a straight line, so they are constantly accelerating inwards, but do not gain additional speed because the accelerating is always done when their motion inwards is zero. However, this is different when pulling the palms closer to the body: The acceleration due to rotation now increases the speed; but because of the rotation, the increase in speed does not translate to a significant speed inwards, but to an increase of the rotation speed.
Stationary-action principle.
In classical mechanics it can be shown that the rotational invariance of action functionals implies conservation of angular momentum. The action is defined in classical physics as a functional of positions, formula_108 often represented by the use of square brackets, and the final and initial times. It assumes the following form in cartesian coordinates:formula_109where the repeated indices indicate summation over the index. If the action is invariant of an infinitesimal transformation, it can be mathematically stated as: formula_110.
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Under the transformation, formula_111, the action becomes:
formula_112
where we can employ the expansion of the terms up-to first order in formula_113:
formula_114giving the following change in action:
formula_115
Since all rotations can be expressed as matrix exponential of skew-symmetric matrices, i.e. as formula_116 where formula_117 is a skew-symmetric matrix and formula_118 is angle of rotation, we can express the change of coordinates due to the rotation formula_119, up-to first order of infinitesimal angle of rotation, formula_120 as:
formula_121
Combining the equation of motion and rotational invariance of action, we get from the above equations that:formula_122Since this is true for any matrix formula_123 that satisfies formula_124 it results in the conservation of the following quantity:
formula_125
as formula_126. This corresponds to the conservation of angular momentum throughout the motion.
Lagrangian formalism.
In Lagrangian mechanics, angular momentum for rotation around a given axis, is the conjugate momentum of the generalized coordinate of the angle around the same axis. For example, formula_127, the angular momentum around the z axis, is:
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formula_128
where formula_129 is the Lagrangian and formula_130 is the angle around the z axis.
Note that formula_131, the time derivative of the angle, is the angular velocity formula_132. Ordinarily, the Lagrangian depends on the angular velocity through the kinetic energy: The latter can be written by separating the velocity to its radial and tangential part, with the tangential part at the x-y plane, around the z-axis, being equal to:
formula_133
where the subscript i stands for the i-th body, and "m", "v""T" and "ω""z" stand for mass, tangential velocity around the z-axis and angular velocity around that axis, respectively.
For a body that is not point-like, with density "ρ", we have instead:
formula_134
where integration runs over the area of the body, and "I"z is the moment of inertia around the z-axis.
Thus, assuming the potential energy does not depend on "ω""z" (this assumption may fail for electromagnetic systems), we have the angular momentum of the "i"th object:
formula_135
We have thus far rotated each object by a separate angle; we may also define an overall angle "θ"z by which we rotate the whole system, thus rotating also each object around the z-axis, and have the overall angular momentum:
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formula_136
From Euler–Lagrange equations it then follows that:
formula_137
Since the lagrangian is dependent upon the angles of the object only through the potential, we have:
formula_138
which is the torque on the "i"th object.
Suppose the system is invariant to rotations, so that the potential is independent of an overall rotation by the angle "θ"z (thus it may depend on the angles of objects only through their differences, in the form formula_139). We therefore get for the total angular momentum:
formula_140
And thus the angular momentum around the z-axis is conserved.
This analysis can be repeated separately for each axis, giving conversation of the angular momentum vector. However, the angles around the three axes cannot be treated simultaneously as generalized coordinates, since they are not independent; in particular, two angles per point suffice to determine its position. While it is true that in the case of a rigid body, fully describing it requires, in addition to three translational degrees of freedom, also specification of three rotational degrees of freedom; however these cannot be defined as rotations around the Cartesian axes (see Euler angles). This caveat is reflected in quantum mechanics in the non-trivial commutation relations of the different components of the angular momentum operator.
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Hamiltonian formalism.
Equivalently, in Hamiltonian mechanics the Hamiltonian can be described as a function of the angular momentum. As before, the part of the kinetic energy related to rotation around the z-axis for the "i"th object is:
formula_141
which is analogous to the energy dependence upon momentum along the z-axis, formula_142.
Hamilton's equations relate the angle around the z-axis to its conjugate momentum, the angular momentum around the same axis:
formula_143
The first equation gives
formula_144
And so we get the same results as in the Lagrangian formalism.
Note, that for combining all axes together, we write the kinetic energy as:
formula_145 is tiny by everyday standards, about 10−34 J s, and therefore this quantization does not noticeably affect the angular momentum of macroscopic objects. However, it is very important in the microscopic world. For example, the structure of electron shells and subshells in chemistry is significantly affected by the quantization of angular momentum.
Quantization of angular momentum was first postulated by Niels Bohr in his model of the atom and was later predicted by Erwin Schrödinger in his Schrödinger equation.
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Uncertainty.
In the definition formula_146, six operators are involved: The position operators formula_147, formula_148, formula_149, and the momentum operators formula_150, formula_151, formula_152. However, the Heisenberg uncertainty principle tells us that it is not possible for all six of these quantities to be known simultaneously with arbitrary precision. Therefore, there are limits to what can be known or measured about a particle's angular momentum. It turns out that the best that one can do is to simultaneously measure both the angular momentum vector's magnitude and its component along one axis.
The uncertainty is closely related to the fact that different components of an angular momentum operator do not commute, for example formula_153. (For the precise commutation relations, see angular momentum operator.)
Total angular momentum as generator of rotations.
As mentioned above, orbital angular momentum L is defined as in classical mechanics: formula_146, but "total" angular momentum J is defined in a different, more basic way: J is defined as the "generator of rotations". More specifically, J is defined so that the operator
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formula_155
is the rotation operator that takes any system and rotates it by angle formula_37 about the axis formula_157. (The "exp" in the formula refers to operator exponential.) To put this the other way around, whatever our quantum Hilbert space is, we expect that the rotation group SO(3) will act on it. There is then an associated action of the Lie algebra so(3) of SO(3); the operators describing the action of so(3) on our Hilbert space are the (total) angular momentum operators.
The relationship between the angular momentum operator and the rotation operators is the same as the relationship between Lie algebras and Lie groups in mathematics. The close relationship between angular momentum and rotations is reflected in Noether's theorem that proves that angular momentum is conserved whenever the laws of physics are rotationally invariant.
Angular momentum in electrodynamics.
When describing the motion of a charged particle in an electromagnetic field, the canonical momentum P (derived from the Lagrangian for this system) is not gauge invariant. As a consequence, the canonical angular momentum L = r × P is not gauge invariant either. Instead, the momentum that is physical, the so-called "kinetic momentum" (used throughout this article), is (in SI units)
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formula_158
where "e" is the electric charge of the particle and A the magnetic vector potential of the electromagnetic field. The gauge-invariant angular momentum, that is "kinetic angular momentum", is given by
formula_159
The interplay with quantum mechanics is discussed further in the article on canonical commutation relations.
Angular momentum in optics.
In "classical Maxwell electrodynamics" the Poynting vector
is a linear momentum density of electromagnetic field.
formula_160
The angular momentum density vector formula_161 is given by a vector product
as in classical mechanics:
formula_162
The above identities are valid "locally", i.e. in each space point formula_48 in a given moment formula_164.
Angular momentum in nature and the cosmos.
Tropical cyclones and other related weather phenomena involve conservation of angular momentum in order to explain the dynamics. Winds revolve slowly around low pressure systems, mainly due to the coriolis effect. If the low pressure intensifies and the slowly circulating air is drawn toward the center, the molecules must speed up in order to conserve angular momentum. By the time they reach the center, the speeds become destructive.
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Johannes Kepler determined the laws of planetary motion without knowledge of conservation of momentum. However, not long after his discovery their derivation was determined from conservation of angular momentum. Planets move more slowly the further they are out in their elliptical orbits, which is explained intuitively by the fact that orbital angular momentum is proportional to the radius of the orbit. Since the mass does not change and the angular momentum is conserved, the velocity drops.
Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (e.g. the Moon) and the primary planet that it orbits (e.g. Earth). The gravitational torque between the Moon and the tidal bulge of Earth causes the Moon to be constantly promoted to a slightly higher orbit (~3.8 cm per year) and Earth to be decelerated (by −25.858 ± 0.003″/cy²) in its rotation (the length of the day increases by ~1.7 ms per century, +2.3 ms from tidal effect and −0.6 ms from post-glacial rebound). The Earth loses angular momentum which is transferred to the Moon such that the overall angular momentum is conserved.
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Angular momentum in engineering and technology.
Examples of using conservation of angular momentum for practical advantage are abundant. In engines such as steam engines or internal combustion engines, a flywheel is needed to efficiently convert the lateral motion of the pistons to rotational motion.
Inertial navigation systems explicitly use the fact that angular momentum is conserved with respect to the inertial frame of space. Inertial navigation is what enables submarine trips under the polar ice cap, but are also crucial to all forms of modern navigation.
Rifled bullets use the stability provided by conservation of angular momentum to be more true in their trajectory. The invention of rifled firearms and cannons gave their users significant strategic advantage in battle, and thus were a technological turning point in history.
History.
Isaac Newton, in the "Principia", hinted at angular momentum in his examples of the first law of motion,A top, whose parts by their cohesion are perpetually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve their motions both progressive and circular for a much longer time.He did not further investigate angular momentum directly in the "Principia", saying:From such kind of reflexions also sometimes arise the circular motions of bodies about their own centers. But these are cases which I do not consider in what follows; and it would be too tedious to demonstrate every particular that relates to this subject.However, his geometric proof of the law of areas is an outstanding example of Newton's genius, and indirectly proves angular momentum conservation in the case of a central force.
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Law of Areas.
Newton's derivation.
As a planet orbits the Sun, the line between the Sun and the planet sweeps out equal areas in equal intervals of time. This had been known since Kepler expounded his second law of planetary motion. Newton derived a unique geometric proof, and went on to show that the attractive force of the Sun's gravity was the cause of all of Kepler's laws.
During the first interval of time, an object is in motion from point A to point B. Undisturbed, it would continue to point c during the second interval. When the object arrives at B, it receives an impulse directed toward point S. The impulse gives it a small added velocity toward S, such that if this were its only velocity, it would move from B to V during the second interval. By the rules of velocity composition, these two velocities add, and point C is found by construction of parallelogram BcCV. Thus the object's path is deflected by the impulse so that it arrives at point C at the end of the second interval. Because the triangles SBc and SBC have the same base SB and the same height Bc or VC, they have the same area. By symmetry, triangle SBc also has the same area as triangle SAB, therefore the object has swept out equal areas SAB and SBC in equal times.
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At point C, the object receives another impulse toward S, again deflecting its path during the third interval from d to D. Thus it continues to E and beyond, the triangles SAB, SBc, SBC, SCd, SCD, SDe, SDE all having the same area. Allowing the time intervals to become ever smaller, the path ABCDE approaches indefinitely close to a continuous curve.
Note that because this derivation is geometric, and no specific force is applied, it proves a more general law than Kepler's second law of planetary motion. It shows that the Law of Areas applies to any central force, attractive or repulsive, continuous or non-continuous, or zero.
Conservation of angular momentum in the law of areas.
The proportionality of angular momentum to the area swept out by a moving object can be understood by realizing that the bases of the triangles, that is, the lines from S to the object, are equivalent to the radius, and that the heights of the triangles are proportional to the perpendicular component of velocity. Hence, if the area swept per unit time is constant, then by the triangular area formula , the product and therefore the product are constant: if and the base length are decreased, and height must increase proportionally. Mass is constant, therefore angular momentum is conserved by this exchange of distance and velocity.
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In the case of triangle SBC, area is equal to (SB)(VC). Wherever C is eventually located due to the impulse applied at B, the product (SB)(VC), and therefore remain constant. Similarly so for each of the triangles.
Another areal proof of conservation of angular momentum for any central force uses Mamikon's sweeping tangents theorem.
After Newton.
Leonhard Euler, Daniel Bernoulli, and Patrick d'Arcy all understood angular momentum in terms of conservation of areal velocity, a result of their analysis of Kepler's second law of planetary motion. It is unlikely that they realized the implications for ordinary rotating matter.
In 1736 Euler, like Newton, touched on some of the equations of angular momentum in his "Mechanica" without further developing them.
Bernoulli wrote in a 1744 letter of a "moment of rotational motion", possibly the first conception of angular momentum as we now understand it.
In 1799, Pierre-Simon Laplace first realized that a fixed plane was associated with rotation—his "invariable plane".
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Louis Poinsot in 1803 began representing rotations as a line segment perpendicular to the rotation, and elaborated on the "conservation of moments".
In 1852 Léon Foucault used a gyroscope in an experiment to display the Earth's rotation.
William J. M. Rankine's 1858 "Manual of Applied Mechanics" defined angular momentum in the modern sense for the first time:... a line whose length is proportional to the magnitude of the angular momentum, and whose direction is perpendicular to the plane of motion of the body and of the fixed point, and such, that when the motion of the body is viewed from the extremity of the line, the radius-vector of the body seems to have right-handed rotation.In an 1872 edition of the same book, Rankine stated that "The term "angular momentum" was introduced by Mr. Hayward," probably referring to R.B. Hayward's article "On a Direct Method of estimating Velocities, Accelerations, and all similar Quantities with respect to Axes moveable in any manner in Space with Applications," which was introduced in 1856, and published in 1864. Rankine was mistaken, as numerous publications feature the term starting in the late 18th to early 19th centuries. However, Hayward's article apparently was the first use of the term and the concept seen by much of the English-speaking world. Before this, angular momentum was typically referred to as "momentum of rotation" in English.
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Plum pudding model
The plum pudding model is an obsolete scientific model of the atom. It was first proposed by J. J. Thomson in 1904 following his discovery of the electron in 1897, and was rendered obsolete by Ernest Rutherford's discovery of the atomic nucleus in 1911. The model tried to account for two properties of atoms then known: that there are electrons, and that atoms have no net electric charge. Logically there had to be an equal amount of positive charge to balance out the negative charge of the electrons. As Thomson had no idea as to the source of this positive charge, he tentatively proposed that it was everywhere in the atom, and that the atom was spherical. This was the mathematically simplest hypothesis to fit the available evidence, or lack thereof. In such a sphere, the negatively charged electrons would distribute themselves in a more or less even manner throughout the volume, simultaneously repelling each other while being attracted to the positive sphere's center.
Despite Thomson's efforts, his model couldn't account for emission spectra and valencies. Based on experimental studies of alpha particle scattering (in the gold foil experiment), Ernest Rutherford developed an alternative model for the atom featuring a compact nucleus where the positive charge is concentrated.
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Thomson's model is popularly referred to as the "plum pudding model" with the notion that the electrons are distributed uniformly like raisins in a plum pudding. Neither Thomson nor his colleagues ever used this analogy. It seems to have been coined by popular science writers to make the model easier to understand for the layman. The analogy is perhaps misleading because Thomson likened the positive sphere to a liquid rather than a solid since he thought the electrons moved around in it.
Significance.
Thomson's model was the first atomic model to describe an internal structure. Before this, atoms were simply the basic units of weight by which the chemical elements combined, and their only properties were valency and relative weight to hydrogen. The model had no properties which concerned physicists, such as electric charge, magnetic moment, volume, or absolute mass, and because of this some physicists had doubted atoms even existed.
Thomson hypothesized that the quantity, arrangement, and motions of electrons in the atom could explain its physical and chemical properties, such as emission spectra, valencies, reactivity, and ionization. He was on the right track, though his approach was based on classical mechanics and he did not have the insight to incorporate quantized energy into it.
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Background.
Throughout the 19th century evidence from chemistry and statistical mechanics accumulated that matter was composed of atoms. The structure of the atom was discussed, and by the end of the century the leading model was the vortex theory of the atom, proposed by William Thomson (later Lord Kelvin) in 1867. By 1890, J.J. Thomson had his own version called the "nebular atom" hypothesis, in which atoms were composed of immaterial vortices and suggested similarities between the arrangement of vortices and periodic regularity found among the chemical elements.
Thomson's discovery of the electron in 1897 changed his views. Thomson called them "corpuscles" (particles), but they were more commonly called "electrons", the name G. J. Stoney had coined for the "fundamental unit quantity of electricity" in 1891. However even late in 1899, few scientists believed in subatomic particles.
Another emerging scientific theme of the 19th century was the discovery and study of radioactivity. Thomson discovered the electron by studying cathode rays, and in 1900 Henri Becquerel determined that the radiation from uranium, now called beta particles, had the same charge/mass ratio as cathode rays. These beta particles were believed to be electrons travelling at high speed. The particles were used by Thomson to probe atoms to find evidence for his atomic theory. The other form of radiation critical to this era of atomic models was alpha particles. Heavier and slower than beta particles, these were the key tool used by Rutherford to find evidence against Thomson's model.
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In addition to the emerging atomic theory, the electron, and radiation, the last element of history was the many studies of atomic spectra published in the late 19th century. Part of the attraction of the vortex model was its possible role in describing the spectral data as vibrational responses to electromagnetic radiation. Neither Thomson's model nor its successor, Rutherford's model, made progress towards understanding atomic spectra. That would have to wait until Niels Bohr built the first quantum-based atom model.
Development.
Thomson's model was the first to assign a specific inner structure to an atom, though his earliest descriptions did not include mathematical formulas.
From 1897 through 1913, Thomson proposed a series of increasingly detailed "polyelectron" models for the atom. His first versions were qualitative culminating in his 1906 paper and follow on summaries. Thomson's model changed over the course of its initial publication, finally becoming a model with much more mobility containing electrons revolving in the dense field of positive charge rather than a static structure. Thomson attempted unsuccessfully to reshape his model to account for some of the major spectral lines experimentally known for several elements.
1897 Corpuscles inside atoms.
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In a paper titled "Cathode Rays", Thomson demonstrated that cathode rays are not light but made of negatively charged particles which he called "corpuscles". He observed that cathode rays can be deflected by electric and magnetic fields, which does not happen with light rays. In a few paragraphs near the end of this long paper Thomson discusses the possibility that atoms were made of these "corpuscles", calling them "primordial atoms". Thomson believed that the intense electric field around the cathode caused the surrounding gas molecules to split up into their component "corpuscles", thereby generating cathode rays. Thomson thus showed evidence that atoms were divisible, though he did not attempt to describe their structure at this point.
Thomson notes that he was not the first scientist to propose that atoms are divisible, making reference to William Prout who in 1815 found that the atomic weights of various elements were multiples of hydrogen's atomic weight and hypothesised that all atoms were made of hydrogen atoms fused together. Prout's hypothesis was dismissed by chemists when by the 1830s it was found that some elements seemed to have a non-integer atomic weight—e.g. chlorine has an atomic weight of about 35.45. But the idea continued to intrigue scientists. The discrepancies were eventually explained with the discovery of isotopes in 1912.
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A few months after Thomson's paper appeared, George FitzGerald suggested that the corpuscle identified by Thomson from cathode rays and proposed as parts of an atom was a "free electron", as described by physicist Joseph Larmor and Hendrik Lorentz. While Thomson did not adopt the terminology, the connection convinced other scientists that cathode rays were particles, an important step in their eventual acceptance of an atomic model based on sub-atomic particles.
In 1899 Thomson reiterated his atomic model in a paper that showed that negative electricity created by ultraviolet light landing on a metal (known now as the photoelectric effect) has the same mass-to-charge ratio as cathode rays; then he applied his previous method for determining the charge on ions to the negative electric particles created by ultraviolet light. He estimated that the electron's mass was 0.0014 times that of the hydrogen ion (as a fraction: ). In the conclusion of this paper he writes:
1904 Mechanical model of the atom.
Thomson provided his first detailed description of the atom in his 1904 paper "On the Structure of the Atom".
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Thomson starts with a short description of his model
... the atoms of the elements consist of a number of negatively electrified corpuscles enclosed in a sphere of uniform positive electrification, ...
Primarily focused on the electrons, Thomson adopted the positive sphere from Kelvin's atom model proposed a year earlier.
He then gives a detailed mechanical analysis of such a system, distributing the electrons uniformly around a ring. The attraction of the positive electrification is balanced by the mutual repulsion of the electrons. His analysis focuses on stability, looking for cases where small changes in position are countered by restoring forces.
After discussing his many formulae for stability he turned to analysing patterns in the number of electrons in various concentric rings of stable configurations. These regular patterns Thomson argued are analogous to the periodic law of chemistry behind the structure of the periodic table. This concept, that a model based on subatomic particles could account for chemical trends, encouraged interest in Thomson's model and influenced future work even if the details Thomson's electron assignments turned out to be incorrect.
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Thomson at this point believed that all the mass of the atom was carried by the electrons. This would mean that even a small atom would have to contain thousands of electrons, and the positive electrification that encapsulated them was without mass.
1905 lecture on electron arrangements.
In a lecture delivered to the Royal Institution of Great Britain in 1905, Thomson explained that it was too computationally difficult for him to calculate the movements of large numbers of electrons in the positive sphere, so he proposed a practical experiment. This involved magnetised pins pushed into cork discs and set afloat in a basin of water. The pins were oriented such that they repelled each other. Above the centre of the basin was suspended an electromagnet that attracted the pins. The equilibrium arrangement the pins took informed Thomson on what arrangements the electrons in an atom might take.
For instance, he observed that while five pins would arrange themselves in a stable pentagon around the centre, six pins could not form a stable hexagon. Instead, one pin would move to the centre and the other five would form a pentagon around the centre pin, and this arrangement was stable. As he added more pins, they would arrange themselves in concentric rings around the centre.
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The experiment functioned in two dimensions instead of three, but Thomson inferred the electrons in the atom arranged themselves in concentric shells and they could move within these shells but did not move from one shell to another them except when electrons were added or subtracted from the atom.
1906 Estimating electrons per atom.
Before 1906 Thomson considered the atomic weight to be due to the mass of the electrons (which he continued to call "corpuscles"). Based on his own estimates of the electron mass, an atom would need tens of thousands electrons to account for the mass. In 1906 he used three different methods, X-ray scattering, beta ray absorption, or optical properties of gases, to estimate that "number of corpuscles is not greatly different from the atomic weight". This reduced the number of electrons to tens or at most a couple of hundred and that in turn meant that the positive sphere in Thomson's model contained most of the mass of the atom. This meant that Thomson's mechanical stability work from 1904 and the comparison to the periodic table were no longer valid. Moreover, the alpha particle, so important to the next advance in atomic theory by Rutherford, would no longer be viewed as an atom containing thousands of electrons.
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In 1907, Thomson published "The Corpuscular Theory of Matter" which reviewed his ideas on the atom's structure and proposed further avenues of research.
In Chapter 6, he further elaborates his experiment using magnetised pins in water, providing an expanded table. For instance, if 59 pins were placed in the pool, they would arrange themselves in concentric rings of the order 20-16-13-8-2 (from outermost to innermost).
In Chapter 7, Thomson summarised his 1906 results on the number of electrons in an atom. He included one important correction: he replaced the beta-particle analysis with one based on the cathode ray experiments of August Becker, giving a result in better agreement with other approaches to the problem. Experiments by other scientists in this field had shown that atoms contain far fewer electrons than Thomson previously thought. Thomson now believed the number of electrons in an atom was a small multiple of its atomic weight: "the number of corpuscles in an atom of any element is proportional to the atomic weight of the element — it is a multiple, and not a large one, of the atomic weight of the element." This meant that almost all of the atom's mass had to be carried by the positive sphere, whatever it was made of.
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Thomson in this book estimated that a hydrogen atom is 1,700 times heavier than an electron (the current measurement is 1,837). Thomson noted that no scientist had yet found a positively charged particle smaller than a hydrogen ion. He also wrote that the positive charge of an atom is a multiple of a basic unit of positive charge, equal to the negative charge of an electron. Thomson refused to jump to the conclusion that the basic unit of positive charge has a mass equal to that of the hydrogen ion, arguing that scientists first had to know how many electrons an atom contains. For all he could tell, a hydrogen ion might still contain a few electrons—perhaps two electrons and three units of positive charge.
1910 Multiple scattering.
Thomson's difficulty with beta scattering in 1906 lead him to renewed interest in the topic. He encouraged J. Arnold Crowther to experiment with beta scattering through thin foils and, in 1910, Thomson produced a new theory of beta scattering. The two innovations in this paper was the introduction of scattering from the positive sphere of the atom and analysis that multiple or compound scattering was critical to the final results. This theory and Crowther's experimental results would be confronted by Rutherford's theory and Geiger and Mardsen new experiments with alpha particles.
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Another innovation in Thomson's 1910 paper was that he modelled how an atom might deflect an incoming beta particle if the positive charge of the atom existed in discrete units of equal but arbitrary size, spread evenly throughout the atom, separated by empty space, with each unit having a positive charge equal to the electron's negative charge. Thomson therefore came close to deducing the existence of the proton, which was something Rutherford eventually did. In Rutherford's model of the atom, the protons are clustered in a very small nucleus, but in Thomson's alternative model, the positive units were spread throughout the atom.
Thomson's 1910 beta scattering model.
In his 1910 paper "On the Scattering of rapidly moving Electrified Particles", Thomson presented equations that modelled how beta particles scatter in a collision with an atom. His work was based on beta scattering studies by James Crowther.
Partial deflection by the positive sphere.
Thomson typically assumed the positive charge in the atom was uniformly distributed throughout its volume, encapsulating the electrons. In his 1910 paper, Thomson presented the following equation which isolated the effect of this positive sphere:
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formula_1
where "k" is the Coulomb constant, "q"e is the charge of the beta particle, "q"g is the charge of the positive sphere, "m" is the mass of the beta particle, and "R" is the radius of the sphere. Because the atom is many thousands of times heavier than the beta particle, no correction for recoil is needed.
Thomson did not explain how this equation was developed, but the historian John L. Heilbron provided an educated guess he called a "straight-line" approximation. Consider a beta particle passing through the positive sphere with its initial trajectory at a lateral distance "b" from the centre. The path is assumed to have a very small deflection and therefore is treated here as a straight line.
Inside a sphere of uniformly distributed positive charge the force exerted on the beta particle at any point along its path through the sphere would be directed along the radius with magnitude:
formula_2
The component of force perpendicular to the trajectory and thus deflecting the path of the particle would be:
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formula_3
The lateral change in momentum "p"y is therefore
formula_4
The resulting angular deflection, formula_5, is given by
formula_6
where "p"x is the average horizontal momentum taken to be equal to the incoming momentum. Since we already know the deflection is very small, we can treat formula_7 as being equal to formula_5.
To find the average deflection angle formula_9, the angle for each value of "b" and the corresponding "L" are added across the face sphere, then divided by the cross-section area. formula_10 per Pythagorean theorem.
formula_11
formula_12
This matches Thomson's formula in his 1910 paper.
Partial deflection by the electrons.
Thomson modelled the collisions between a beta particle and the electrons of an atom by calculating the deflection of one collision then multiplying by a factor for the number of collisions as the particle crosses the atom.
For the electrons within an arbitrary distance "s" of the beta particle's path, their mean distance will be . Therefore, the average deflection per electron will be
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formula_13
where "q"e is the elementary charge, "k" is the Coulomb constant, "m" and "v" are the mass and velocity of the beta particle.
The factor for the number of collisions was known to be the square root of the number of possible electrons along path. The number of electrons depends upon the density of electrons along the particle path times the path length "L".
The net deflection caused by all the electrons within this arbitrary cylinder of effect around the beta particle's path is
formula_14
where "N"0 is the number of electrons per unit volume and formula_15 is the volume of this cylinder.
Since Thomson calculated the deflection would be very small, he treats "L" as a straight line. Therefore formula_16 where "b" is the distance of this chord from the centre. The mean of formula_17 is given by the integral
formula_18
We can now replace formula_17 in the equation for formula_20 to obtain the mean deflection formula_21:
formula_22
formula_23
where "N" is the number of electrons in the atom, equal to formula_24.
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Deflection by the positive charge in discrete units.
In his 1910 paper, Thomson proposed an alternative model in which the positive charge exists in discrete units separated by empty space, with those units being evenly distributed throughout the atom's volume.
In this concept, the average scattering angle of the beta particle is given by:
formula_25
where "σ" is the ratio of the volume occupied by the positive charge to the volume of the whole atom. Thomson did not explain how he arrived at this equation.
Net deflection.
To find the combined effect of the positive charge and the electrons on the beta particle's path, Thomson provided the following equation:
formula_26
Demise of the plum pudding model.
Thomson probed the structure of atoms through beta particle scattering, whereas his former student Ernest Rutherford was interested in alpha particle scattering. Beta particles are electrons emitted by radioactive decay, whereas alpha particles are essentially helium atoms, also emitted in process of decay. Alpha particles have considerably more momentum than beta particles and Rutherford found that matter scatters alpha particles in ways that Thomson's plum pudding model could not predict.
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Between 1908 and 1913, Ernest Rutherford, Hans Geiger, and Ernest Marsden collaborated on a series of experiments in which they bombarded thin metal foils with a beam of alpha particles and measured the intensity versus scattering angle of the particles. They found that the metal foil could scatter alpha particles by more than 90°. This should not have been possible according to the Thomson model: the scattering into large angles should have been negligible. The odds of a beta particle being scattered by more than 90° under such circumstances is astronomically small, and since alpha particles typically have much more momentum than beta particles, their deflection should be smaller still. The Thomson models simply could not produce electrostatic forces of sufficient strength to cause such large deflection. The charges in the Thomson model were too diffuse. This led Rutherford to discard the Thomson for a new model where the positive charge of the atom is concentrated in a tiny nucleus.
Rutherford went on to make more compelling discoveries. In Thomson's model, the positive charge sphere was just an abstract component, but Rutherford found something concrete to attribute the positive charge to: particles he dubbed "protons". Whereas Thomson believed that the electron count was roughly correlated to the atomic weight, Rutherford showed that (in a neutral atom) it is exactly equal to the atomic number.
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Thomson hypothesised that the arrangement of the electrons in the atom somehow determined the spectral lines of a chemical element. He was on the right track, but it had nothing to do with how atoms circulated in a sphere of positive charge. Scientists eventually discovered that it had to do with how electrons absorb and release energy in discrete quantities, moving through energy levels which correspond to emission and absorption spectra. Thomson had not incorporated quantum mechanics into his atomic model, which at the time was a very new field of physics. Niels Bohr and Erwin Schroedinger later incorporated quantum mechanics into the atomic model.
Rutherford's nuclear model.
Rutherford's 1911 paper on alpha particle scattering showed that Thomson's scattering model could not explain the large angle scattering and it showed that multiple scattering was not necessary to explain the data. However, in the years immediately following its publication few scientists took note. The scattering model predictions were not considered definitive evidence against Thomson's plum pudding model. Thomson and Rutherford had pioneered scattering as a technique to probe atoms, its reliability and value were unproven. Before Rutherford's paper the alpha particle was considered an atom, not a compact mass. It was not clear why it should be a good probe. Moreover, Rutherford's paper did not discuss the atomic electrons vital to practical problems like chemistry or atomic spectroscopy. Rutherford's nuclear model would only become widely accepted after the work of Niels Bohr.
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Mathematical Thomson problem.
The Thomson problem in mathematics seeks the optimal distribution of equal point charges on the surface of a sphere. Unlike the original Thomson atomic model, the sphere in this purely mathematical model does not have a charge, and this causes all the point charges to move to the surface of the sphere by their mutual repulsion. There is still no general solution to Thomson's original problem of how electrons arrange themselves within a sphere of positive charge.
Origin of the nickname.
The first known writer to compare Thomson's model to a plum pudding was an anonymous reporter in an article for the British pharmaceutical magazine "The Chemist and Druggist" in August 1906.
The analogy was never used by Thomson nor his colleagues. It seems to have been coined by popular science writers to make the model easier to understand for the layman.
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History of atomic theory
Atomic theory is the scientific theory that matter is composed of particles called atoms. The definition of the word "atom" has changed over the years in response to scientific discoveries. Initially, it referred to a hypothetical concept of there being some fundamental particle of matter, too small to be seen by the naked eye, that could not be divided. Then the definition was refined to being the basic particles of the chemical elements, when chemists observed that elements seemed to combine with each other in ratios of small whole numbers. Then physicists discovered that these particles had an internal structure of their own and therefore perhaps did not deserve to be called "atoms", but renaming atoms would have been impractical by that point.
Atomic theory is one of the most important scientific developments in history, crucial to all the physical sciences. At the start of "The Feynman Lectures on Physics", physicist and Nobel laureate Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept.
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Philosophical atomism.
The basic idea that matter is made up of tiny indivisible particles is an old idea that appeared in many ancient cultures. The word "atom" is derived from the ancient Greek word "atomos", which means "uncuttable". This ancient idea was based in philosophical reasoning rather than scientific reasoning. Modern atomic theory is not based on these old concepts. In the early 19th century, the scientist John Dalton noticed that chemical substances seemed to combine with each other by discrete and consistent units of weight, and he decided to use the word "atom" to refer to these units.
Groundwork.
Working in the late 17th century, Robert Boyle developed the concept of a chemical element as substance different from a compound.
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Dalton's law of multiple proportions.
John Dalton studied data gathered by himself and by other scientists. He noticed a pattern that later came to be known as the law of multiple proportions: in compounds which contain two particular elements, the amount of Element A per measure of Element B will differ across these compounds by ratios of small whole numbers. This suggested that each element combines with other elements in multiples of a basic quantity.
In 1804, Dalton explained his atomic theory to his friend and fellow chemist Thomas Thomson, who published an explanation of Dalton's theory in his book "A System of Chemistry" in 1807. According to Thomson, Dalton's idea first occurred to him when experimenting with "olefiant gas" (ethylene) and "carburetted hydrogen gas" (methane). Dalton found that "carburetted hydrogen gas" contains twice as much hydrogen per measure of carbon as "olefiant gas", and concluded that a molecule of "olefiant gas" is one carbon atom and one hydrogen atom, and a molecule of "carburetted hydrogen gas" is one carbon atom and two hydrogen atoms. In reality, an ethylene molecule has two carbon atoms and four hydrogen atoms (C2H4), and a methane molecule has one carbon atom and four hydrogen atoms (CH4). In this particular case, Dalton was mistaken about the formulas of these compounds, but he got them right in the following examples:
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Example 1 — tin oxides: Dalton identified two types of tin oxide. One is a grey powder that Dalton referred to as "the protoxide of tin", which is 88.1% tin and 11.9% oxygen. The other is a white powder which Dalton referred to as "the deutoxide of tin", which is 78.7% tin and 21.3% oxygen. Adjusting these figures, in the grey powder there is about 13.5 g of oxygen for every 100 g of tin, and in the white powder there is about 27 g of oxygen for every 100 g of tin. 13.5 and 27 form a ratio of 1:2. These compounds are known today as tin(II) oxide (SnO) and tin(IV) oxide (SnO2). In Dalton's terminology, a "protoxide" is a molecule containing a single oxygen atom, and a "deutoxide" molecule has two. The modern equivalents of his terms would be "monoxide" and "dioxide".
Example 2 — iron oxides: Dalton identified two oxides of iron. There is one type of iron oxide that is a black powder which Dalton referred to as "the protoxide of iron", which is 78.1% iron and 21.9% oxygen. The other iron oxide is a red powder, which Dalton referred to as "the intermediate or red oxide of iron" which is 70.4% iron and 29.6% oxygen. Adjusting these figures, in the black powder there is about 28 g of oxygen for every 100 g of iron, and in the red powder there is about 42 g of oxygen for every 100 g of iron. 28 and 42 form a ratio of 2:3. These compounds are iron(II) oxide and iron(III) oxide and their formulas are FeO and Fe2O3 respectively. Iron(II) oxide's formula is normally written as FeO, but since it is a crystalline substance one could alternately write it as Fe2O2, and when we contrast that with Fe2O3, the 2:3 ratio stands out plainly. Dalton described the "intermediate oxide" as being "2 atoms protoxide and 1 of oxygen", which adds up to two atoms of iron and three of oxygen. That averages to one and a half atoms of oxygen for every iron atom, putting it midway between a "protoxide" and a "deutoxide".
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Example 3 — nitrogen oxides: Dalton was aware of three oxides of nitrogen: "nitrous oxide", "nitrous gas", and "nitric acid". These compounds are known today as nitrous oxide, nitric oxide, and nitrogen dioxide respectively. "Nitrous oxide" is 63.3% nitrogen and 36.7% oxygen, which means it has 80 g of oxygen for every 140 g of nitrogen. "Nitrous gas" is 44.05% nitrogen and 55.95% oxygen, which means there is 160 g of oxygen for every 140 g of nitrogen. "Nitric acid" is 29.5% nitrogen and 70.5% oxygen, which means it has 320 g of oxygen for every 140 g of nitrogen. 80 g, 160 g, and 320 g form a ratio of 1:2:4. The formulas for these compounds are N2O, NO, and NO2.
Dalton defined an atom as being the "ultimate particle" of a chemical substance, and he used the term "compound atom" to refer to "ultimate particles" which contain two or more elements. This is inconsistent with the modern definition, wherein an atom is the basic particle of a chemical element and a molecule is an agglomeration of atoms. The term "compound atom" was confusing to some of Dalton's contemporaries as the word "atom" implies indivisibility, but he responded that if a carbon dioxide "atom" is divided, it ceases to be carbon dioxide. The carbon dioxide "atom" is indivisible in the sense that it cannot be divided into smaller carbon dioxide particles.
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Dalton made the following assumptions on how "elementary atoms" combined to form "compound atoms" (what we today refer to as molecules). When two elements can only form one compound, he assumed it was one atom of each, which he called a "binary compound". If two elements can form two compounds, the first compound is a binary compound and the second is a "ternary compound" consisting of one atom of the first element and two of the second. If two elements can form three compounds between them, then the third compound is a "quaternary" compound containing one atom of the first element and three of the second. Dalton thought that water was a "binary compound", i.e. one hydrogen atom and one oxygen atom. Dalton did not know that in their natural gaseous state, the ultimate particles of oxygen, nitrogen, and hydrogen exist in pairs (O2, N2, and H2). Nor was he aware of valencies. These properties of atoms were discovered later in the 19th century.
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Opposition to atomic theory.
Dalton's atomic theory attracted widespread interest but not everyone accepted it at first. The law of multiple proportions was shown not to be a universal law when it came to organic substances, whose molecules can be quite large. For instance, in oleic acid there is 34 g of hydrogen for every 216 g of carbon, and in methane there is 72 g of hydrogen for every 216 g of carbon. 34 and 72 form a ratio of 17:36, which is not a ratio of small whole numbers. We know now that carbon-based substances can have very large molecules, larger than any the other elements can form. Oleic acid's formula is C18H34O2 and methane's is CH4. The law of multiple proportions by itself was not complete proof, and atomic theory was not universally accepted until the end of the 19th century.
One problem was the lack of uniform nomenclature. The word "atom" implied indivisibility, but Dalton defined an atom as being the ultimate particle of any chemical substance, not just the elements or even matter per se. This meant that "compound atoms" such as carbon dioxide could be divided, as opposed to "elementary atoms". Dalton disliked the word "molecule", regarding it as "diminutive". Amedeo Avogadro did the opposite: he exclusively used the word "molecule" in his writings, eschewing the word "atom", instead using the term "elementary molecule". Jöns Jacob Berzelius used the term "organic atoms" to refer to particles containing three or more elements, because he thought this only existed in organic compounds. Jean-Baptiste Dumas used the terms "physical atoms" and "chemical atoms"; a "physical atom" was a particle that cannot be divided by physical means such as temperature and pressure, and a "chemical atom" was a particle that could not be divided by chemical reactions.
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The modern definitions of "atom" and "molecule"—an atom being the basic particle of an element, and a molecule being an agglomeration of atoms—were established in the late half of the 19th century. A key event was the Karlsruhe Congress in Germany in 1860. As the first international congress of chemists, its goal was to establish some standards in the community. A major proponent of the modern distinction between atoms and molecules was Stanislao Cannizzaro.
Cannizzaro criticized past chemists such as Berzelius for not accepting that the particles of certain gaseous elements are actually pairs of atoms, which led to mistakes in their formulation of certain compounds. Berzelius believed that hydrogen gas and chlorine gas particles are solitary atoms. But he observed that when one liter of hydrogen reacts with one liter of chlorine, they form two liters of hydrogen chloride instead of one. Berzelius decided that Avogadro's law does not apply to compounds. Cannizzaro preached that if scientists just accepted the existence of single-element molecules, such discrepancies in their findings would be easily resolved. But Berzelius did not even have a word for that. Berzelius used the term "elementary atom" for a gas particle which contained just one element and "compound atom" for particles which contained two or more elements, but there was nothing to distinguish H2 from H since Berzelius did not believe in H2. So Cannizzaro called for a redefinition so that scientists could understand that a hydrogen "molecule" can split into two hydrogen "atoms" in the course of a chemical reaction.
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A second objection to atomic theory was philosophical. Scientists in the 19th century had no way of directly observing atoms. They inferred the existence of atoms through indirect observations, such as Dalton's law of multiple proportions. Some scientists adopted positions aligned with the philosophy of positivism, arguing that scientists should not attempt to deduce the deeper reality of the universe, but only systemize what patterns they could directly observe.
This generation of anti-atomists can be grouped in two camps.
The "equivalentists", like Marcellin Berthelot, believed the theory of equivalent weights was adequate for scientific purposes. This generalization of Proust's law of definite proportions summarized observations. For example, 1 gram of hydrogen will combine with 8 grams of oxygen to form 9 grams of water, therefore the "equivalent weight" of oxygen is 8 grams. The "energeticist", like Ernst Mach and Wilhelm Ostwald, were philosophically opposed to hypothesis about reality altogether. In their view, only energy as part of thermodynamics should be the basis of physical models.
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These positions were eventually quashed by two important advancements that happened later in the 19th century: the development of the periodic table and the discovery that molecules have an internal architecture that determines their properties.
Isomerism.
Scientists discovered some substances have the exact same chemical content but different properties. For instance, in 1827, Friedrich Wöhler discovered that silver fulminate and silver cyanate are both 107 parts silver, 12 parts carbon, 14 parts nitrogen, and 16 parts oxygen (we now know their formulas as both AgCNO). In 1830 Jöns Jacob Berzelius introduced the term "isomerism" to describe the phenomenon. In 1860, Louis Pasteur hypothesized that the molecules of isomers might have the same set of atoms but in different arrangements.
In 1874, Jacobus Henricus van 't Hoff proposed that the carbon atom bonds to other atoms in a tetrahedral arrangement. Working from this, he explained the structures of organic molecules in such a way that he could predict how many isomers a compound could have. Consider, for example, pentane (C5H12). In van 't Hoff's way of modelling molecules, there are three possible configurations for pentane, and scientists did go on to discover three and only three isomers of pentane.
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Isomerism was not something that could be fully explained by alternative theories to atomic theory, such as radical theory and the theory of types.
Mendeleev's periodic table.
Dmitrii Mendeleev noticed that when he arranged the elements in a row according to their atomic weights, there was a certain periodicity to them. For instance, the second element, lithium, had similar properties to the ninth element, sodium, and the sixteenth element, potassium — a period of seven. Likewise, beryllium, magnesium, and calcium were similar and all were seven places apart from each other on Mendeleev's table. Using these patterns, Mendeleev predicted the existence and properties of new elements, which were later discovered in nature: scandium, gallium, and germanium. Moreover, the periodic table could predict how many atoms of other elements that an atom could bond with — e.g., germanium and carbon are in the same group on the table and their atoms both combine with two oxygen atoms each (GeO2 and CO2). Mendeleev found these patterns validated atomic theory because it showed that the elements could be categorized by their atomic weight. Inserting a new element into the middle of a period would break the parallel between that period and the next, and would also violate Dalton's law of multiple proportions.
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The elements on the periodic table were originally arranged in order of increasing atomic weight. However, in a number of places chemists chose to swap the positions of certain adjacent elements so that they appeared in a group with other elements with similar properties. For instance, tellurium is placed before iodine even though tellurium is heavier (127.6 vs 126.9) so that iodine can be in the same column as the other halogens. The modern periodic table is based on atomic number, which is equivalent to the nuclear charge, a change had to wait for the discovery of the nucleus.
In addition, an entire row of the table was not shown
because the noble gases had not been discovered when Mendeleev devised his table.
Statistical mechanics.
In 1738, Swiss physicist and mathematician Daniel Bernoulli postulated that the pressure of gases and heat were both caused by the underlying motion of particles. Using his model he could predict the ideal gas law at constant temperature and suggested that the temperature was proportional to the velocity of the particles. These results were largely ignored for a century.
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James Clerk Maxwell, a vocal proponent of atomism, revived the kinetic theory in 1860 and 1867. His key insight was that the velocity of particles in a gas would vary around an average value, introducing the concept of a distribution function. Ludwig Boltzmann and Rudolf Clausius expanded his work on gases and the laws of thermodynamics especially the second law relating to entropy. In the 1870s, Josiah Willard Gibbs extended the laws of entropy and thermodynamics and coined the term "statistical mechanics."
Boltzmann defended the atomistic hypothesis against major detractors from the time like Ernst Mach or energeticists like Wilhelm Ostwald, who considered that energy was the elementary quantity of reality.
At the beginning of the 20th century, Albert Einstein independently reinvented Gibbs' laws, because they had only been printed in an obscure American journal. Einstein later commented that had he known of Gibbs' work, he would "not have published those papers at all, but confined myself to the treatment of some few points [that were distinct]." All of statistical mechanics and the laws of heat, gas, and entropy took the existence of atoms as a necessary postulate.
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Brownian motion.
In 1827, the British botanist Robert Brown observed that dust particles inside pollen grains floating in water constantly jiggled about for no apparent reason. In 1905, Einstein theorized that this Brownian motion was caused by the water molecules continuously knocking the grains about, and developed a mathematical model to describe it. This model was validated experimentally in 1908 by French physicist Jean Perrin, who used Einstein's equations to measure the size of atoms.
Discovery of the electron.
Atoms were thought to be the smallest possible division of matter until 1899 when J. J. Thomson discovered the electron through his work on cathode rays.
A Crookes tube is a sealed glass container in which two electrodes are separated by a vacuum. When a voltage is applied across the electrodes, cathode rays are generated, creating a glowing patch where they strike the glass at the opposite end of the tube. Through experimentation, Thomson discovered that the rays could be deflected by electric fields and magnetic fields, which meant that these rays were not a form of light but were composed of very light charged particles, and their charge was negative. Thomson called these particles "corpuscles". He measured their mass-to-charge ratio to be several orders of magnitude smaller than that of the hydrogen atom, the smallest atom. This ratio was the same regardless of what the electrodes were made of and what the trace gas in the tube was.
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In contrast to those corpuscles, positive ions created by electrolysis or X-ray radiation had mass-to-charge ratios that varied depending on the material of the electrodes and the type of gas in the reaction chamber, indicating they were different kinds of particles.
In 1898, Thomson measured the charge on ions to be roughly 6 × 10−10 electrostatic units (2 × 10−19 Coulombs). In 1899, he showed that negative electricity created by ultraviolet light landing on a metal (known now as the photoelectric effect) has the same mass-to-charge ratio as cathode rays; then he applied his previous method for determining the charge on ions to the negative electric particles created by ultraviolet light. By this combination he showed that electron's mass was 0.0014 times that of hydrogen ions. These "corpuscles" were so light yet carried so much charge that Thomson concluded they must be the basic particles of electricity, and for that reason other scientists decided that these "corpuscles" should instead be called electrons following an 1894 suggestion by George Johnstone Stoney for naming the basic unit of electrical charge.
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In 1904, Thomson published a paper describing a new model of the atom. Electrons reside within atoms, and they transplant themselves from one atom to the next in a chain in the action of an electrical current. When electrons do not flow, their negative charge logically must be balanced out by some source of positive charge within the atom so as to render the atom electrically neutral. Having no clue as to the source of this positive charge, Thomson tentatively proposed that the positive charge was everywhere in the atom, the atom being shaped like a sphere—this was the mathematically simplest model to fit the available evidence (or lack of it). The balance of electrostatic forces would distribute the electrons throughout this sphere in a more or less even manner. Thomson further explained that ions are atoms that have a surplus or shortage of electrons.
Thomson's model is popularly known as the plum pudding model, based on the idea that the electrons are distributed throughout the sphere of positive charge with the same density as raisins in a plum pudding. Neither Thomson nor his colleagues ever used this analogy. It seems to have been a conceit of popular science writers. The analogy suggests that the positive sphere is like a solid, but Thomson likened it to a liquid, as he proposed that the electrons moved around in it in patterns governed by the electrostatic forces. Thus the positive electrification in Thomson's model was a temporary concept. Thomson's model was incomplete, it could not predict any of the known properties of the atom such as emission spectra or valencies.
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In 1906, Robert A. Millikan and Harvey Fletcher performed the oil drop experiment in which they measured the charge of an electron to be about -1.6 × 10−19, a value now defined as -1 "e". Since the hydrogen ion and the electron were known to be indivisible and a hydrogen atom is neutral in charge, it followed that the positive charge in hydrogen was equal to this value, i.e. 1 "e".
Discovery of the nucleus.
Thomson's plum pudding model was challenged in 1911 by one of his former students, Ernest Rutherford, who presented a new model to explain new experimental data. The new model proposed a concentrated center of charge and mass that was later dubbed the atomic nucleus.
Ernest Rutherford and his colleagues Hans Geiger and Ernest Marsden came to have doubts about the Thomson model after they encountered difficulties when they tried to build an instrument to measure the charge-to-mass ratio of alpha particles (these are positively-charged particles emitted by certain radioactive substances such as radium). The alpha particles were being scattered by the air in the detection chamber, which made the measurements unreliable. Thomson had encountered a similar problem in his work on cathode rays, which he solved by creating a near-perfect vacuum in his instruments. Rutherford didn't think he'd run into this same problem because alpha particles usually have much more momentum than electrons. According to Thomson's model of the atom, the positive charge in the atom is not concentrated enough to produce an electric field strong enough to deflect an alpha particle. Yet there was scattering, so Rutherford and his colleagues decided to investigate this scattering carefully.
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Between 1908 and 1913, Rutherford and his colleagues performed a series of experiments in which they bombarded thin foils of metal with a beam of alpha particles. They spotted alpha particles being deflected by angles greater than 90°. According to Thomson's model, all of the alpha particles should have passed through with negligible deflection. Rutherford deduced that the positive charge of the atom is not distributed throughout the atom's volume as Thomson believed, but is concentrated in a tiny nucleus at the center. This nucleus also carries most of the atom's mass. Only such an intense concentration of charge, anchored by its high mass, could produce an electric field strong enough to deflect the alpha particles as observed. Rutherford's model, being supported primarily by scattering data unfamiliar to many scientists, did not catch on until Niels Bohr joined Rutherford's lab and developed a new model for the electrons.
Rutherford model predicted that the scattering of alpha particles would be proportional to the square of the atomic charge. Geiger and Marsden's based their analysis on setting the charge to half of the atomic weight of the foil's material (gold, aluminium, etc.). Amateur physicist Antonius van den Broek noted that there was a more precise relation between the charge and the element's numeric sequence in the order of atomic weights. The sequence number came be called the atomic number and it replaced atomic weight in organizing the periodic table.
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Bohr model.
Rutherford deduced the existence of the atomic nucleus through his experiments but he had nothing to say about how the electrons were arranged around it. In 1912, Niels Bohr joined Rutherford's lab and began his work on a quantum model of the atom.
Max Planck in 1900 and Albert Einstein in 1905 had postulated that light energy is emitted or absorbed in discrete amounts known as quanta (singular, "quantum"). This led to a series of atomic models with some quantum aspects, such as that of Arthur Erich Haas in 1910 and the 1912 John William Nicholson atomic model with quantized angular momentum as "h"/2. The dynamical structure of these models was still classical, but in 1913, Bohr abandon the classical approach. He started his Bohr model of the atom with a quantum hypothesis: an electron could only orbit the nucleus in particular circular orbits with fixed angular momentum and energy, its distance from the nucleus (i.e., their radii) being proportional to its energy. Under this model an electron could not lose energy in a continuous manner; instead, it could only make instantaneous "quantum leaps" between the fixed energy levels. When this occurred, light was emitted or absorbed at a frequency proportional to the change in energy (hence the absorption and emission of light in discrete spectra).
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In a trilogy of papers Bohr described and applied his model to derive the Balmer series of lines in the atomic spectrum of hydrogen and the related spectrum of He+. He also used he model to describe the structure of the periodic table and aspects of chemical bonding. Together these results lead to Bohr's model being widely accepted by the end of 1915.
Bohr's model was not perfect. It could only predict the spectral lines of hydrogen, not those of multielectron atoms. Worse still, it could not even account for all features of the hydrogen spectrum: as spectrographic technology improved, it was discovered that applying a magnetic field caused spectral lines to multiply in a way that Bohr's model couldn't explain. In 1916, Arnold Sommerfeld added elliptical orbits to the Bohr model to explain the extra emission lines, but this made the model very difficult to use, and it still couldn't explain more complex atoms.
Discovery of isotopes.
While experimenting with the products of radioactive decay, in 1913 radiochemist Frederick Soddy discovered that there appeared to be more than one variety of some elements. The term isotope was coined by Margaret Todd as a suitable name for these varieties.
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That same year, J. J. Thomson conducted an experiment in which he channeled a stream of neon ions through magnetic and electric fields, striking a photographic plate at the other end. He observed two glowing patches on the plate, which suggested two different deflection trajectories. Thomson concluded this was because some of the neon ions had a different mass. The nature of this differing mass would later be explained by the discovery of neutrons in 1932: all atoms of the same element contain the same number of protons, while different isotopes have different numbers of neutrons.
Discovery of the proton.
Back in 1815, William Prout observed that the atomic weights of the known elements were multiples of hydrogen's atomic weight, so he hypothesized that all atoms are agglomerations of hydrogen, a particle which he dubbed "the protyle". Prout's hypothesis was put into doubt when some elements were found to deviate from this pattern—e.g. chlorine atoms on average weigh 35.45 daltons—but when isotopes were discovered in 1913, Prout's observation gained renewed attention.
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In 1898, J. J. Thomson found that the positive charge of a hydrogen ion was equal to the negative charge of a single electron.
In an April 1911 paper concerning his studies on alpha particle scattering, Ernest Rutherford estimated that the charge of an atomic nucleus, expressed as a multiplier of hydrogen's nuclear charge ("q"e), is roughly half the atom's atomic weight.
In June 1911, Van den Broek noted that on the periodic table, each successive chemical element increased in atomic weight on average by 2, which in turn suggested that each successive element's nuclear charge increased by 1 "q"e. In 1913, van den Broek further proposed that the electric charge of an atom's nucleus, expressed as a multiplier of the elementary charge, is equal to the element's sequential position on the periodic table. Rutherford defined this position as being the element's atomic number.
In 1913, Henry Moseley measured the X-ray emissions of all the elements on the periodic table and found that the frequency of the X-ray emissions was a mathematical function of the element's atomic number and the charge of a hydrogen nucleus .
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In 1917 Rutherford bombarded nitrogen gas with alpha particles and observed hydrogen ions being emitted from the gas. Rutherford concluded that the alpha particles struck the nuclei of the nitrogen atoms, causing hydrogen ions to split off.
These observations led Rutherford to conclude that the hydrogen nucleus was a singular particle with a positive charge equal to that of the electron's negative charge. The name "proton" was suggested by Rutherford at an informal meeting of fellow physicists in Cardiff in 1920.
The charge number of an atomic nucleus was found to be equal to the element's ordinal position on the periodic table. The nuclear charge number thus provided a simple and clear-cut way of distinguishing the chemical elements from each other, as opposed to Lavoisier's classic definition of a chemical element being a substance that cannot be broken down into simpler substances by chemical reactions. The charge number or proton number was thereafter referred to as the atomic number of the element. In 1923, the International Committee on Chemical Elements officially declared the atomic number to be the distinguishing quality of a chemical element.
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During the 1920s, some writers defined the atomic number as being the number of "excess protons" in a nucleus. Before the discovery of the neutron, scientists believed that the atomic nucleus contained a number of "nuclear electrons" which cancelled out the positive charge of some of its protons. This explained why the atomic weights of most atoms were higher than their atomic numbers. Helium, for instance, was thought to have four protons and two nuclear electrons in the nucleus, leaving two excess protons and a net nuclear charge of 2+. After the neutron was discovered, scientists realized the helium nucleus in fact contained two protons and two neutrons.
Discovery of the neutron.
Physicists in the 1920s believed that the atomic nucleus contained protons plus a number of "nuclear electrons" that reduced the overall charge. These "nuclear electrons" were distinct from the electrons that orbited the nucleus. This incorrect hypothesis would have explained why the atomic numbers of the elements were less than their atomic weights, and why radioactive elements emit electrons (beta radiation) in the process of nuclear decay. Rutherford even hypothesized that a proton and an electron could bind tightly together into a "neutral doublet". Rutherford wrote that the existence of such "neutral doublets" moving freely through space would provide a more plausible explanation for how the heavier elements could have formed in the genesis of the Universe, given that it is hard for a lone proton to fuse with a large atomic nucleus because of the repulsive electric field.
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In 1928, Walter Bothe observed that beryllium emitted a highly penetrating, electrically neutral radiation when bombarded with alpha particles. It was later discovered that this radiation could knock hydrogen atoms out of paraffin wax. Initially it was thought to be high-energy gamma radiation, since gamma radiation had a similar effect on electrons in metals, but James Chadwick found that the ionization effect was too strong for it to be due to electromagnetic radiation, so long as energy and momentum were conserved in the interaction. In 1932, Chadwick exposed various elements, such as hydrogen and nitrogen, to the mysterious "beryllium radiation", and by measuring the energies of the recoiling charged particles, he deduced that the radiation was actually composed of electrically neutral particles which could not be massless like the gamma ray, but instead were required to have a mass similar to that of a proton. Chadwick called this new particle "the neutron" and believed that it to be a proton and electron fused together because the neutron had about the same mass as a proton and an electron's mass is negligible by comparison. Neutrons are not in fact a fusion of a proton and an electron.
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Modern quantum mechanical models.
In 1924, Louis de Broglie proposed that all particles—particularly subatomic particles such as electrons—have an associated wave. Erwin Schrödinger, fascinated by this idea, developed an equation that describes an electron as a wave function instead of a point. This approach predicted many of the spectral phenomena that Bohr's model failed to explain, but it was difficult to visualize, and faced opposition. One of its critics, Max Born, proposed instead that Schrödinger's wave function did not describe the physical extent of an electron (like a charge distribution in classical electromagnetism), but rather gave the probability that an electron would, when measured, be found at a particular point. This reconciled the ideas of wave-like and particle-like electrons: the behavior of an electron, or of any other subatomic entity, has both wave-like and particle-like aspects, and whether one aspect or the other is observed depend upon the experiment.
A consequence of describing particles as waveforms rather than points is that it is mathematically impossible to calculate with precision both the position and momentum of a particle at a given point in time. This became known as the uncertainty principle, a concept first introduced by Werner Heisenberg in 1927.
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Schrödinger's wave model for hydrogen replaced Bohr's model, with its neat, clearly defined circular orbits. The modern model of the atom describes the positions of electrons in an atom in terms of probabilities. An electron can potentially be found at any distance from the nucleus, but, depending on its energy level and angular momentum, exists more frequently in certain regions around the nucleus than others; this pattern is referred to as its atomic orbital. The orbitals come in a variety of shapes—sphere, dumbbell, torus, etc.—with the nucleus in the middle. The shapes of atomic orbitals are found by solving the Schrödinger equation. Analytic solutions of the Schrödinger equation are known for very few relatively simple model Hamiltonians including the hydrogen atom and the hydrogen molecular ion. Beginning with the helium atom—which contains just two electrons—numerical methods are used to solve the Schrödinger equation.
Qualitatively the shape of the atomic orbitals of multi-electron atoms resemble the states of the hydrogen atom. The Pauli principle requires the distribution of these electrons within the atomic orbitals such that no more than two electrons are assigned to any one orbital; this requirement profoundly affects the atomic properties and ultimately the bonding of atoms into molecules.
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Ai
AI most frequently refers to artificial intelligence, which is intelligence demonstrated by machines.
Ai, AI or A.I. may also refer to:
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Aung San Suu Kyi
Aung San Suu Kyi (born 19 June 1945) is a Burmese politician, diplomat, author, and political activist who served as State Counsellor of Myanmar and Minister of Foreign Affairs from 2016 to 2021. She has served as the general secretary of the National League for Democracy (NLD) since the party's founding in 1988 and was registered as its chairperson while it was a legal party from 2011 to 2023. She played a vital role in Myanmar's transition from military junta to partial democracy in the 2010s.
The youngest daughter of Aung San, Father of the Nation of modern-day Myanmar, and Khin Kyi, Aung San Suu Kyi was born in Rangoon, British Burma. After graduating from the University of Delhi in 1964 and St Hugh's College, Oxford in 1968, she worked at the United Nations for three years. She married Michael Aris in 1972, with whom she had two children.
Aung San Suu Kyi rose to prominence in the 8888 Uprising of 8 August 1988 and became the General Secretary of the NLD, which she had newly formed with the help of several retired army officials who criticised the military junta. In the 1990 general election, NLD won 81% of the seats in Parliament, but the results were nullified, as the State Peace and Development Council (SPDC), the military government, refused to hand over power, resulting in an international outcry. She had been detained before the elections and remained under house arrest for almost 15 of the 21 years from 1989 to 2010, becoming one of the world's most prominent political prisoners. In 1999, "Time" magazine named her one of the "Children of Gandhi" and his spiritual heir to nonviolence. She survived an assassination attempt in the 2003 Depayin massacre when at least 70 people associated with the NLD were killed.
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Her party boycotted the 2010 general election, resulting in a decisive victory for the military-backed Union Solidarity and Development Party (USDP). Aung San Suu Kyi became a member of the Pyithu Hluttaw (House of Representatives) while her party won 43 of the 45 vacant seats in the 2012 by-elections. In the 2015 general election, her party won a landslide victory, taking 86% of the seats in the Pyidaungsu Hluttaw, well more than the 67% supermajority needed to ensure that its preferred candidates were elected president and vice president in the Presidential Electoral College. Although she was prohibited from becoming the president due to a clause in the Myanmar Constitution—her late husband and children are foreign citizens—she assumed the newly created role of State Counsellor of Myanmar, a role akin to a prime minister or a head of government.
When she ascended to the office of state counsellor, Aung San Suu Kyi drew criticism from several countries, organisations and figures over Myanmar's inaction in response to the Rohingya genocide in Rakhine State and refusal to acknowledge that the Tatmadaw (armed forces) had committed massacres. Under her leadership, Myanmar also drew criticism for prosecutions of journalists. In 2019, Aung San Suu Kyi appeared in the International Court of Justice where she defended the Myanmar military against allegations of genocide against the Rohingya people.
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Aung San Suu Kyi, whose party had won the November 2020 general election, was arrested on 1 February 2021 following a coup d'état that returned the Tatmadaw to power and sparked protests across the country. Several charges were filed against her, and on 6 December 2021, she was sentenced to four years in prison on two of them. Later, on 10 January 2022, she was sentenced to an additional four years on another set of charges. On 12 October 2022, she was convicted of two further charges of corruption and she was sentenced to two terms of three years' imprisonment to be served concurrent to each other. On 30 December 2022, her trials ended with another conviction and an additional sentence of seven years' imprisonment for corruption. Aung San Suu Kyi's final sentence was of 33 years in prison, later reduced to 27 years. The United Nations, most European countries, and the United States condemned the arrests, trials, and sentences as politically motivated.
Name.
"Aung San Suu Kyi", like other Burmese names, includes no surname, but is only a personal name, in her case derived from three relatives: "Aung San" from her father, "Suu" from her paternal grandmother, and "Kyi" from her mother Khin Kyi.
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In Myanmar, Aung San Suu Kyi is often referred to as "Daw" Aung San Suu Kyi. "Daw", literally meaning "aunt", is not part of her name but is an honorific for any older and revered woman, akin to "Madam". She is sometimes addressed as Daw Suu or Amay Suu ("Mother Suu") by her supporters.
Personal life.
Aung San Suu Kyi was born on 19 June 1945 in Rangoon (now Yangon), British Burma. According to Peter Popham, she was born in a small village outside Rangoon called Hmway Saung. Her father, Aung San, allied with the Japanese during World War II. Aung San founded the modern Burmese army and negotiated Burma's independence from the United Kingdom in 1947; he was assassinated by his rivals in the same year. She is a niece of Thakin Than Tun who was the husband of Khin Khin Gyi, the elder sister of her mother Khin Kyi.
She grew up with her mother, Khin Kyi, and two brothers, Aung San Lin and Aung San Oo, in Rangoon. Aung San Lin died at the age of eight when he drowned in an ornamental lake on the grounds of the house. Her elder brother emigrated to San Diego, California, becoming a United States citizen. After Aung San Lin's death, the family moved to a house by Inya Lake where Aung San Suu Kyi met people of various backgrounds, political views, and religions. She was educated in Methodist English High School (now Basic Education High School No. 1 Dagon) for much of her childhood in Burma, where she was noted as having a talent for learning languages. She speaks four languages: Burmese, English (with a British accent), French, and Japanese. She is a Theravada Buddhist.
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Aung San Suu Kyi's mother, Khin Kyi, gained prominence as a political figure in the newly formed Burmese government. She was appointed Burmese ambassador to India and Nepal in 1960, and Aung San Suu Kyi followed her there. She studied in the Convent of Jesus and Mary School in New Delhi, and graduated from Lady Shri Ram College, a constituent college of the University of Delhi in New Delhi, with a degree in politics in 1964. Suu Kyi continued her education at St Hugh's College, Oxford, obtaining a B.A. degree in Philosophy, Politics and Economics in 1967, graduating with a third-class degree that was promoted per tradition to an MA in 1968. After graduating, she lived in New York City with family friend Ma Than E, who was once a popular Burmese pop singer. She worked at the United Nations for three years, primarily on budget matters, writing daily to her future husband, Dr. Michael Aris. On 1 January 1972, Aung San Suu Kyi and Aris, a scholar of Tibetan culture and literature, living abroad in Bhutan, were married. The following year, she gave birth to their first son, Alexander Aris, in London; their second son, Kim Aris, was born in 1977. Between 1985 and 1987, Aung San Suu Kyi was working toward a Master of Philosophy degree in Burmese literature as a research student at the School of Oriental and African Studies (SOAS), University of London. She was elected as an Honorary Fellow of St Hugh's in 1990. For two years, she was a Fellow at the Indian Institute of Advanced Studies (IIAS) in Shimla, India. She also worked for the government of the Union of Burma.
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In 1988, Aung San Suu Kyi returned to Burma to tend for her ailing mother. Aris' visit in Christmas 1995 was the last time that he and Aung San Suu Kyi met, as she remained in Burma and the Burmese dictatorship denied him any further entry visas. Aris was diagnosed with prostate cancer in 1997 which was later found to be terminal. Despite appeals from prominent figures and organisations, including the United States, UN Secretary-General Kofi Annan and Pope John Paul II, the Burmese government would not grant Aris a visa, saying that they did not have the facilities to care for him, and instead urged Aung San Suu Kyi to leave the country to visit him. She was at that time temporarily free from house arrest but was unwilling to depart, fearing that she would be refused re-entry if she left, as she did not trust the military junta's assurance that she could return.
Aris died on his 53rd birthday on 27 March 1999. Since 1989, when his wife was first placed under house arrest, he had seen her only five times, the last of which was for Christmas in 1995. She was also separated from her children, who live in the United Kingdom, until 2011.
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On 2 May 2008, after Cyclone Nargis hit Burma, Aung San Suu Kyi's dilapidated lakeside bungalow lost its roof and electricity, while the cyclone also left entire villages in the Irrawaddy delta submerged. Plans to renovate and repair the house were announced in August 2009. Aung San Suu Kyi was released from house arrest on 13 November 2010.
Political career.
Political beginning.
Coincidentally, when Aung San Suu Kyi returned to Burma in 1988, the long-time military leader of Burma and head of the ruling party, General Ne Win, stepped down. Mass demonstrations for democracy followed that event on 8 August 1988 (8–8–88, a day seen as auspicious), which were violently suppressed in what came to be known as the 8888 Uprising. On 24 August 1988, she made her first public appearance at the Yangon General Hospital, addressing protestors from a podium. On 26 August, she addressed half a million people at a mass rally in front of the Shwedagon Pagoda in the capital, calling for a democratic government. However, in September 1988, a new military junta took power.
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Influenced by both Mahatma Gandhi's philosophy of non-violence and also by the Buddhist concepts, Aung San Suu Kyi entered politics to work for democratisation, helped found the National League for Democracy on 27 September 1988, but was put under house arrest on 20 July 1989. She was offered freedom if she left the country, but she refused. Despite her philosophy of non-violence, a group of ex-military commanders and senior politicians who joined NLD during the crisis believed that she was too confrontational and left NLD. However, she retained enormous popularity and support among NLD youths with whom she spent most of her time.
During the crisis, the previous democratically elected Prime Minister of Burma, U Nu, initiated to form an interim government and invited opposition leaders to join him. Indian Prime Minister Rajiv Gandhi had signaled his readiness to recognize the interim government. However, Aung San Suu Kyi categorically rejected U Nu's plan by saying "the future of the opposition would be decided by masses of the people". Ex-Brigadier General Aung Gyi, another influential politician at the time of the 8888 Uprising and the first chairman in the history of the NLD, followed the suit and rejected the plan after Aung San Suu Kyi's refusal. Aung Gyi later accused several NLD members of being communists and resigned from the party.
1990 general election and Nobel Peace Prize.
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In 1990, the military junta called a general election, in which the NLD received 59% of the votes, guaranteeing NLD 80% of the parliament seats. Some claim that Aung San Suu Kyi would have assumed the office of Prime Minister. Instead, the results were nullified and the military refused to hand over power, resulting in an international outcry. Aung San Suu Kyi was placed under house arrest at her home on University Avenue () in Rangoon, during which time she was awarded the Sakharov Prize for Freedom of Thought in 1990, and the Nobel Peace Prize one year later. Her sons Alexander and Kim Aris accepted the Nobel Peace Prize on her behalf. Aung San Suu Kyi used the Nobel Peace Prize's US$1.3 million prize money to establish a health and education trust for the Burmese people. Around this time, Aung San Suu Kyi chose non-violence as an expedient political tactic, stating in 2007, "I do not hold to nonviolence for moral reasons, but for political and practical reasons."
The decision of the Nobel Committee mentions:
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In 1995 Aung San Suu Kyi delivered the keynote address at the Fourth World Conference on Women in Beijing.
1996 attack.
On 9 November 1996, the motorcade that Aung San Suu Kyi was traveling in with other National League for Democracy leaders Tin Oo and Kyi Maung, was attacked in Yangon. About 200 men swooped down on the motorcade, wielding metal chains, metal batons, stones and other weapons. The car that Aung San Suu Kyi was in had its rear window smashed, and the car with Tin Oo and Kyi Maung had its rear window and two backdoor windows shattered. It is believed the offenders were members of the Union Solidarity and Development Association (USDA) who were allegedly paid Ks.500/- (@ USD $0.50) each to participate. The NLD lodged an official complaint with the police, and according to reports the government launched an investigation, but no action was taken. (Amnesty International 120297)
House arrest.
Aung San Suu Kyi was placed under house arrest for a total of 15 years over a 21-year period, on numerous occasions, since she began her political career, during which time she was prevented from meeting her party supporters and international visitors. In an interview, she said that while under house arrest she spent her time reading philosophy, politics and biographies that her husband had sent her. She also passed the time playing the piano and was occasionally allowed visits from foreign diplomats as well as from her personal physician.
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Although under house arrest, Aung San Suu Kyi was granted permission to leave Burma under the condition that she never return, which she refused: "As a mother, the greater sacrifice was giving up my sons, but I was always aware of the fact that others had given up more than me. I never forget that my colleagues who are in prison suffer not only physically, but mentally for their families who have no security outside—in the larger prison of Burma under authoritarian rule."
The media were also prevented from visiting Aung San Suu Kyi, as occurred in 1998 when Italian journalist Maurizio Giuliano, after photographing her, was stopped by customs officials who then confiscated all his films, tapes and some notes. In contrast, Aung San Suu Kyi did have visits from government representatives, such as during her autumn 1994 house arrest when she met the leader of Burma, Senior General Than Shwe and General Khin Nyunt on 20 September in the first meeting since she had been placed in detention. On several occasions during her house arrest, she had periods of poor health and as a result was hospitalised.
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The Burmese government detained and kept Aung San Suu Kyi imprisoned because it viewed her as someone "likely to undermine the community peace and stability" of the country, and used both Article 10(a) and 10(b) of the 1975 State Protection Act (granting the government the power to imprison people for up to five years without a trial), and Section 22 of the "Law to Safeguard the State Against the Dangers of Those Desiring to Cause Subversive Acts" as legal tools against her. She continuously appealed her detention, and many nations and figures continued to call for her release and that of 2,100 other political prisoners in the country. On 12 November 2010, days after the junta-backed Union Solidarity and Development Party (USDP) won elections conducted after a gap of 20 years, the junta finally agreed to sign orders allowing Aung San Suu Kyi's release, and her house arrest term came to an end on 13 November 2010.
United Nations involvement.
The United Nations (UN) has attempted to facilitate dialogue between the junta and Aung San Suu Kyi. On 6 May 2002, following secret confidence-building negotiations led by the UN, the government released her; a government spokesman said that she was free to move "because we are confident that we can trust each other". Aung San Suu Kyi proclaimed "a new dawn for the country". However, on 30 May 2003 in an incident similar to the 1996 attack on her, a government-sponsored mob attacked her caravan in the northern village of Depayin, murdering and wounding many of her supporters. Aung San Suu Kyi fled the scene with the help of her driver, Kyaw Soe Lin, but was arrested upon reaching Ye-U. The government imprisoned her at Insein Prison in Rangoon. After she underwent a hysterectomy in September 2003, the government again placed her under house arrest in Rangoon.
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The results from the UN facilitation have been mixed; Razali Ismail, UN special envoy to Burma, met with Aung San Suu Kyi. Ismail resigned from his post the following year, partly because he was denied re-entry to Burma on several occasions. Several years later in 2006, Ibrahim Gambari, UN Undersecretary-General (USG) of Department of Political Affairs, met with Aung San Suu Kyi, the first visit by a foreign official since 2004. He also met with her later the same year. On 2 October 2007 Gambari returned to talk to her again after seeing Than Shwe and other members of the senior leadership in Naypyidaw. State television broadcast Aung San Suu Kyi with Gambari, stating that they had met twice. This was Aung San Suu Kyi's first appearance in state media in the four years since her current detention began.
The United Nations Working Group for Arbitrary Detention published an Opinion that Aung San Suu Kyi's deprivation of liberty was arbitrary and in contravention of Article 9 of the Universal Declaration of Human Rights 1948, and requested that the authorities in Burma set her free, but the authorities ignored the request at that time. The U.N. report said that according to the Burmese Government's reply, "Daw Aung San Suu Kyi has not been arrested, but has only been taken into protective custody, for her own safety", and while "it could have instituted legal action against her under the country's domestic legislation ... it has preferred to adopt a magnanimous attitude, and is providing her with protection in her own interests".
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Such claims were rejected by Brigadier-General Khin Yi, Chief of Myanmar Police Force (MPF). On 18 January 2007, the state-run paper "New Light of Myanmar" accused Aung San Suu Kyi of tax evasion for spending her Nobel Prize money outside the country. The accusation followed the defeat of a US-sponsored United Nations Security Council resolution condemning Burma as a threat to international security; the resolution was defeated because of strong opposition from China, which has strong ties with the military junta (China later voted against the resolution, along with Russia and South Africa).
In November 2007, it was reported that Aung San Suu Kyi would meet her political allies National League for Democracy along with a government minister. The ruling junta made the official announcement on state TV and radio just hours after UN special envoy Ibrahim Gambari ended his second visit to Burma. The NLD confirmed that it had received the invitation to hold talks with Aung San Suu Kyi. However, the process delivered few concrete results.
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On 3 July 2009, UN Secretary-General Ban Ki-moon went to Burma to pressure the junta into releasing Aung San Suu Kyi and to institute democratic reform. However, on departing from Burma, Ban Ki-moon said he was "disappointed" with the visit after junta leader Than Shwe refused permission for him to visit Aung San Suu Kyi, citing her ongoing trial. Ban said he was "deeply disappointed that they have missed a very important opportunity".
2007 anti-government protests.
Protests led by Buddhist monks during Saffron Revolution began on 19 August 2007 following steep fuel price increases, and continued each day, despite the threat of a crackdown by the military.
On 22 September 2007, although still under house arrest, Aung San Suu Kyi made a brief public appearance at the gate of her residence in Yangon to accept the blessings of Buddhist monks who were marching in support of human rights. It was reported that she had been moved the following day to Insein Prison (where she had been detained in 2003), but meetings with UN envoy Ibrahim Gambari near her Rangoon home on 30 September and 2 October established that she remained under house arrest.
2009 trespass incident.
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On 3 May 2009, an American man, identified as John Yettaw, swam across Inya Lake to her house uninvited and was arrested when he made his return trip three days later. He had attempted to make a similar trip two years earlier, but for unknown reasons was turned away. He later claimed at trial that he was motivated by a divine vision requiring him to notify her of an impending terrorist assassination attempt. On 13 May, Aung San Suu Kyi was arrested for violating the terms of her house arrest because the swimmer, who pleaded exhaustion, was allowed to stay in her house for two days before he attempted the swim back. Aung San Suu Kyi was later taken to Insein Prison, where she could have faced up to five years' confinement for the intrusion. The trial of Aung San Suu Kyi and her two maids began on 18 May and a small number of protesters gathered outside. Diplomats and journalists were barred from attending the trial; however, on one occasion, several diplomats from Russia, Thailand and Singapore and journalists were allowed to meet Aung San Suu Kyi. The prosecution had originally planned to call 22 witnesses. It also accused John Yettaw of embarrassing the country. During the ongoing defence case, Aung San Suu Kyi said she was innocent. The defence was allowed to call only one witness (out of four), while the prosecution was permitted to call 14 witnesses. The court rejected two character witnesses, NLD members Tin Oo and Win Tin, and permitted the defence to call only a legal expert. According to one unconfirmed report, the junta was planning to, once again, place her in detention, this time in a military base outside the city. In a separate trial, Yettaw said he swam to Aung San Suu Kyi's house to warn her that her life was "in danger". The national police chief later confirmed that Yettaw was the "main culprit" in the case filed against Aung San Suu Kyi. According to aides, Aung San Suu Kyi spent her 64th birthday in jail sharing biryani rice and chocolate cake with her guards.
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Her arrest and subsequent trial received worldwide condemnation by the UN Secretary General Ban Ki-moon, the United Nations Security Council, Western governments, South Africa, Japan and the Association of Southeast Asian Nations, of which Burma is a member. The Burmese government strongly condemned the statement, as it created an "unsound tradition" and criticised Thailand for meddling in its internal affairs. The Burmese Foreign Minister Nyan Win was quoted in the state-run newspaper "New Light of Myanmar" as saying that the incident "was trumped up to intensify international pressure on Burma by internal and external anti-government elements who do not wish to see the positive changes in those countries' policies toward Burma". Ban responded to an international campaign by flying to Burma to negotiate, but Than Shwe rejected all of his requests.
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Late 2000s: International support for release.
Aung San Suu Kyi has received vocal support from Western nations in Europe, Australia and North and South America, as well as India, Israel, Japan the Philippines and South Korea. In December 2007, the US House of Representatives voted unanimously 400–0 to award Aung San Suu Kyi the Congressional Gold Medal; the Senate concurred on 25 April 2008. On 6 May 2008, President George W. Bush signed legislation awarding Aung San Suu Kyi the Congressional Gold Medal. She is the first recipient in American history to receive the prize while imprisoned. More recently, there has been growing criticism of her detention by Burma's neighbours in the Association of Southeast Asian Nations (ASEAN), particularly from Indonesia, Thailand, the Philippines and Singapore. At one point Malaysia warned Burma that it faced expulsion from ASEAN as a result of the detention of Aung San Suu Kyi. Other nations including South Africa, Bangladesh and the Maldives also called for her release. The United Nations has urged the country to move towards inclusive national reconciliation, the restoration of democracy, and full respect for human rights. In December 2008, the United Nations General Assembly passed a resolution condemning the human rights situation in Burma and calling for Aung San Suu Kyi's release—80 countries voting for the resolution, 25 against and 45 abstentions. Other nations, such as China and Russia, are less critical of the regime and prefer to cooperate only on economic matters. Indonesia has urged China to push Burma for reforms. However, Samak Sundaravej, former Prime Minister of Thailand, criticised the amount of support for Aung San Suu Kyi, saying that "Europe uses Aung San Suu Kyi as a tool. If it's not related to Aung San Suu Kyi, you can have deeper discussions with Myanmar."
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Vietnam, however, did not support calls by other ASEAN member states for Myanmar to free Aung San Suu Kyi, state media reported Friday, 14 August 2009. The state-run Việt Nam News said Vietnam had no criticism of Myanmar's decision 11 August 2009 to place Aung San Suu Kyi under house arrest for the next 18 months, effectively barring her from elections scheduled for 2010. "It is our view that the Aung San Suu Kyi trial is an internal affair of Myanmar", Vietnamese government spokesman Le Dung stated on the website of the Ministry of Foreign Affairs. In contrast with other ASEAN member states, Dung said Vietnam has always supported Myanmar and hopes it will continue to implement the "roadmap to democracy" outlined by its government.
Nobel Peace Prize winners (Archbishop Desmond Tutu, the Dalai Lama, Shirin Ebadi, Adolfo Pérez Esquivel, Mairead Corrigan, Rigoberta Menchú, Prof. Elie Wiesel, US President Barack Obama, Betty Williams, Jody Williams and former US President Jimmy Carter) called for the rulers of Burma to release Aung San Suu Kyi to "create the necessary conditions for a genuine dialogue with Daw Aung San Suu Kyi and all concerned parties and ethnic groups to achieve an inclusive national reconciliation with the direct support of the United Nations". Some of the money she received as part of the award helped fund higher education grants to Burmese students through the London-based charity Prospect Burma.
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It was announced prior to the 2010 Burmese general election that Aung San Suu Kyi may be released "so she can organize her party", However, Aung San Suu Kyi was not allowed to run. On 1 October 2010 the government announced that she would be released on 13 November 2010.
US President Barack Obama personally advocated the release of all political prisoners, especially Aung San Suu Kyi, during the US-ASEAN Summit of 2009.
The US Government hoped that successful general elections would be an optimistic indicator of the Burmese government's sincerity towards eventual democracy. The Hatoyama government which spent 2.82 billion yen in 2008, has promised more Japanese foreign aid to encourage Burma to release Aung San Suu Kyi in time for the elections; and to continue moving towards democracy and the rule of law.
In a personal letter to Aung San Suu Kyi, UK Prime Minister Gordon Brown cautioned the Burmese government of the potential consequences of rigging elections as "condemning Burma to more years of diplomatic isolation and economic stagnation".
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Aung San Suu Kyi met with many heads of state and opened a dialog with the Minister of Labor Aung Kyi (not to be confused with Aung San Suu Kyi). She was allowed to meet with senior members of her NLD party at the State House, however these meetings took place under close supervision.
2010 release.
On the evening of 13 November 2010, Aung San Suu Kyi was released from house arrest. This was the date her detention had been set to expire according to a court ruling in August 2009 and came six days after a widely criticised general election. She appeared in front of a crowd of her supporters, who rushed to her house in Rangoon when nearby barricades were removed by the security forces. Aung San Suu Kyi had been detained for 15 of the past 21 years. The government newspaper "New Light of Myanmar" reported the release positively, saying she had been granted a pardon after serving her sentence "in good conduct". "The New York Times" suggested that the military government may have released Aung San Suu Kyi because it felt it was in a confident position to control her supporters after the election.
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Her son Kim Aris was granted a visa in November 2010 to see his mother shortly after her release, for the first time in 10 years. He visited again on 5 July 2011, to accompany her on a trip to Bagan, her first trip outside Yangon since 2003. Her son visited again on 8 August 2011, to accompany her on a trip to Pegu, her second trip.
Discussions were held between Aung San Suu Kyi and the Burmese government during 2011, which led to a number of official gestures to meet her demands. In October, around a tenth of Burma's political prisoners were freed in an amnesty and trade unions were legalised.
In November 2011, following a meeting of its leaders, the NLD announced its intention to re-register as a political party to contend 48 by-elections necessitated by the promotion of parliamentarians to ministerial rank. Following the decision, Aung San Suu Kyi held a telephone conference with US President Barack Obama, in which it was agreed that Secretary of State Hillary Clinton would make a visit to Burma, a move received with caution by Burma's ally China. On 1 December 2011, Aung San Suu Kyi met with Hillary Clinton at the residence of the top-ranking US diplomat in Yangon.
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On 21 December 2011, Thai Prime Minister Yingluck Shinawatra met Aung San Suu Kyi in Yangon, marking Aung San Suu Kyi's "first-ever meeting with the leader of a foreign country".
On 5 January 2012, British Foreign Minister William Hague met Aung San Suu Kyi and his Burmese counterpart. This represented a significant visit for Aung San Suu Kyi and Burma. Aung San Suu Kyi studied in the UK and maintains many ties there, whilst Britain is Burma's largest bilateral donor.
During Aung San Suu Kyi's visit to Europe, she visited the Swiss parliament, collected her 1991 Nobel Prize in Oslo and her honorary degree from the University of Oxford.
2012 by-elections.
In December 2011, there was speculation that Aung San Suu Kyi would run in the 2012 national by-elections to fill vacant seats. On 18 January 2012, Aung San Suu Kyi formally registered to contest a Pyithu Hluttaw (lower house) seat in the Kawhmu Township constituency in special parliamentary elections to be held on 1 April 2012. The seat was previously held by Soe Tint, who vacated it after being appointed Construction Deputy Minister, in the 2010 election. She ran against Union Solidarity and Development Party candidate Soe Min, a retired army physician and native of Twante Township.
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On 3 March 2012, at a large campaign rally in Mandalay, Aung San Suu Kyi unexpectedly left after 15 minutes, because of exhaustion and airsickness.
In an official campaign speech broadcast on Burmese state television's MRTV on 14 March 2012, Aung San Suu Kyi publicly campaigned for reform of the 2008 Constitution, removal of restrictive laws, more adequate protections for people's democratic rights, and establishment of an independent judiciary. The speech was leaked online a day before it was broadcast. A paragraph in the speech, focusing on the Tatmadaw's repression by means of law, was censored by authorities.
Aung San Suu Kyi also called for international media to monitor the by-elections, while publicly pointing out irregularities in official voter lists, which include deceased individuals and exclude other eligible voters in the contested constituencies. On 21 March 2012, Aung San Suu Kyi was quoted as saying "Fraud and rule violations are continuing and we can even say they are increasing."
When asked whether she would assume a ministerial post if given the opportunity, she said the following:
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