ceaglex/VisualTTS_Chem · Datasets at Hugging Face

text stringlengths 19 206
OTQOaH4nAto-034\|I said it looks like the electron can delocalize over the length of the molecule.
OTQOaH4nAto-035\|It's as if the electron is trapped in a little box that's the length of the molecule.
OTQOaH4nAto-036\|So the electron has probability all along that molecule, just like the particle in a box that we talked about before.
OTQOaH4nAto-041\|So let's just remind ourselves of the particle in a box wave functions.
OTQOaH4nAto-042\|Here they are.
OTQOaH4nAto-046\|So the energy levels for a particle in a box, we should remember a couple of things.
OTQOaH4nAto-047\|One is as the box gets bigger, the energy levels go as n squared over l squared.
OTQOaH4nAto-048\|Will l is the length, so longer boxes, the energy levels start to come closer together.
OTQOaH4nAto-049\|They get closer together.
OTQOaH4nAto-050\|And when you get to a very big box, the energy levels are stacked right on top of each other and virtually become continuous.
OTQOaH4nAto-051\|And that's where you'd make the transition from quantum mechanical to classical.
OTQOaH4nAto-052\|In a very large box or big particles you'd have continuous energy levels.
OTQOaH4nAto-053\|You wouldn't have quantized velocities for a marble rolling around in a box.
OTQOaH4nAto-054\|It can go at any velocity.
OTQOaH4nAto-055\|A quantum mechanical particle has quantized energies.
OTQOaH4nAto-056\|So small boxes, I have spacing between my energy levels.
OTQOaH4nAto-060\|So a big particle in a box, a macroscopic particle or a marble rolling around in a box, you could bring to a stop at its lowest energy level.
OTQOaH4nAto-061\|Quantum mechanical particles don't stop.
rCVJLXWD1ng-000\|Let's talk about ionization energies now that we understand a little bit about effective nuclear charge and shielding.
rCVJLXWD1ng-001\|Which atom or iron has the lowest ionization energy-- a hydrogen in the excited 2p state?
rCVJLXWD1ng-002\|A helium plus in the excited 3p state?
rCVJLXWD1ng-003\|Or lithium plus 2 in the excited 4p state?
rCVJLXWD1ng-010\|We're talking about three species, and we're trying to determine the ionization energy.
rCVJLXWD1ng-013\|So let's just do that.
rCVJLXWD1ng-014\|For hydrogen in the 2p state, z is 1, charge in the nucleus, n is 2, so we'll have a quarter of a Rydberg to ionize.
rCVJLXWD1ng-017\|We have 9/16 of a Rydberg, a little more than half a Rydberg to ionize.
luB5a39kGkA-000\|Particles can have wave-like properties.
luB5a39kGkA-001\|If the momentum is small enough, a moving particle displays the properties of a wave.
luB5a39kGkA-002\|We can actually demonstrate it.
luB5a39kGkA-005\|So electrons that behave like waves plus boundaries gives you quantization.
luB5a39kGkA-006\|Now we need to look at that in an interesting situation.
luB5a39kGkA-007\|We've looked at a particle in a one-dimensional box.
luB5a39kGkA-008\|What about an atom?
luB5a39kGkA-009\|An atom is an electron bound by the nucleus.
luB5a39kGkA-010\|An electric charge holds the electron about the nucleus.
luB5a39kGkA-011\|So that's a particle that behaves like a wave, plus boundaries on where it has to be in space.
luB5a39kGkA-012\|That should lead to quantized energy levels for the electron.
luB5a39kGkA-013\|So let's look at that carefully.
luB5a39kGkA-014\|First, we'll have to describe three-dimensional space in terms of easy parameters for quantum mechanical calculations.
luB5a39kGkA-015\|We'll do that using something called spherical polar coordinates.
luB5a39kGkA-018\|So we'll get regions of space, just like in the particle in a box, where the particle is more likely to be located.
luB5a39kGkA-019\|So let's look at these spherical polar coordinates.
luB5a39kGkA-020\|How do we describe where an electron is about an atom?
luB5a39kGkA-021\|Well, it's somewhere about the nucleus in three-dimensional space.
luB5a39kGkA-022\|We'll draw a vector from the center of the coordinate system, which is where the nucleus will be, out to the electron.
luB5a39kGkA-023\|And it'll have length r.
luB5a39kGkA-024\|That will be our first coordinate, the length r.
luB5a39kGkA-025\|Then we'll take the angle from the positive z-axis out to that vector r.
luB5a39kGkA-026\|That will be the angle theta.
luB5a39kGkA-027\|That's our second coordinate.
luB5a39kGkA-028\|And then we'll take a third coordinate, the angle of the projection into the xy plane of the vector, and that'll be our third coordinate, phi.
luB5a39kGkA-029\|So r, theta, phi.
luB5a39kGkA-030\|Three coordinates for three dimensions of space.
luB5a39kGkA-033\|For three dimensions, we'll get three quantum numbers, one for each dimension.
luB5a39kGkA-034\|So those quantum numbers will be n, l, and m sub l.
luB5a39kGkA-035\|Let's look at those quantum numbers and how they relate to the properties of the wave function.
luB5a39kGkA-036\|So we'll look at the quantum number values and the orbital property.
luB5a39kGkA-037\|Now I'm going to start to use the term orbital.
luB5a39kGkA-038\|What I mean is wave function, or square of the wave function.
luB5a39kGkA-039\|The orbital is the region in space where the electron can exist.
luB5a39kGkA-040\|So that's what the wave function describes.
luB5a39kGkA-041\|I'll use those two terms interchangeably.
luB5a39kGkA-042\|So quantum number.
luB5a39kGkA-043\|First, the principle quantum number, n, just like in a particle in a box, has values 1, 2, 3, and describes the overall energy of the system.
luB5a39kGkA-044\|And just like in the particle in a box, when you have the total number of nodes, n minus 1, you know how high your energy is.
luB5a39kGkA-045\|More nodes, more energy.
luB5a39kGkA-046\|Now-- or a higher energy system.
luB5a39kGkA-047\|Now remember node.
luB5a39kGkA-048\|That's an area where the wave function goes to zero.
luB5a39kGkA-049\|The square of the wave function is zero.
luB5a39kGkA-052\|So the larger n, the more values of l you have.
luB5a39kGkA-053\|So l starts at zero.
luB5a39kGkA-054\|Now it's our first zero value quantum number.
luB5a39kGkA-055\|And it counts up in integers up to n minus 1.
luB5a39kGkA-056\|So if n is 3, l could be 0, 1, or 2.
luB5a39kGkA-057\|That's n minus 1.
luB5a39kGkA-058\|Now for l, we'll also use letter designations.
luB5a39kGkA-059\|Now I know sometimes in chemistry you're thinking, you're throwing this nomenclature at me just to make it confusing.
luB5a39kGkA-060\|And unfortunately for the s, p, and d designations, I don't have a good answer for you.
luB5a39kGkA-061\|They're historical designations of these values of l, and you just have to memorize them.
luB5a39kGkA-062\|It is kind of almost a confusion factor that we're going to throw in on top of this.
luB5a39kGkA-063\|Sometimes the quantum numbers will be a number, and sometimes it's going to be a letter.
luB5a39kGkA-064\|So memorize these values for l.
luB5a39kGkA-065\|L tells you the overall shape of the orbital, the shape of the wave function.
luB5a39kGkA-066\|Is it dumbbell shaped?
luB5a39kGkA-067\|Is it spherical shape?
luB5a39kGkA-068\|Is it elongated?
luB5a39kGkA-069\|Is it narrow?
luB5a39kGkA-070\|Those kind of things come from l.
luB5a39kGkA-072\|And it will have values ranging from minus l to l.
luB5a39kGkA-073\|So if l is 2, you'll go minus 2, minus 1, 0, 1, 2.
luB5a39kGkA-074\|From minus l to l in integer steps.
luB5a39kGkA-075\|So there could be many values of m sub l for a given value of l.
luB5a39kGkA-076\|And it's going to tell you something about the orientation.
luB5a39kGkA-077\|If I have a dumbbell shaped, maybe along the x-axis, maybe I'm along the z-axis.
luB5a39kGkA-078\|M sub l will help you determine that.
luB5a39kGkA-079\|So we're not going to look at the actual values of the wave function, the mathematical formulas.
luB5a39kGkA-080\|What we will look at is the values of the quantum numbers.
luB5a39kGkA-081\|Each set of quantum numbers describes an individual wave function.
luB5a39kGkA-082\|Just like in a particle in a box when you took n equal 1, that was a single hump function.

OTQOaH4nAto-034|I said it looks like the electron can delocalize over the length of the molecule.

OTQOaH4nAto-035|It's as if the electron is trapped in a little box that's the length of the molecule.

OTQOaH4nAto-036|So the electron has probability all along that molecule, just like the particle in a box that we talked about before.

OTQOaH4nAto-041|So let's just remind ourselves of the particle in a box wave functions.

OTQOaH4nAto-042|Here they are.

OTQOaH4nAto-046|So the energy levels for a particle in a box, we should remember a couple of things.

OTQOaH4nAto-047|One is as the box gets bigger, the energy levels go as n squared over l squared.

OTQOaH4nAto-048|Will l is the length, so longer boxes, the energy levels start to come closer together.

OTQOaH4nAto-049|They get closer together.

OTQOaH4nAto-050|And when you get to a very big box, the energy levels are stacked right on top of each other and virtually become continuous.

OTQOaH4nAto-051|And that's where you'd make the transition from quantum mechanical to classical.

OTQOaH4nAto-052|In a very large box or big particles you'd have continuous energy levels.

OTQOaH4nAto-053|You wouldn't have quantized velocities for a marble rolling around in a box.

OTQOaH4nAto-054|It can go at any velocity.

OTQOaH4nAto-055|A quantum mechanical particle has quantized energies.

OTQOaH4nAto-056|So small boxes, I have spacing between my energy levels.

OTQOaH4nAto-060|So a big particle in a box, a macroscopic particle or a marble rolling around in a box, you could bring to a stop at its lowest energy level.

OTQOaH4nAto-061|Quantum mechanical particles don't stop.

rCVJLXWD1ng-000|Let's talk about ionization energies now that we understand a little bit about effective nuclear charge and shielding.

rCVJLXWD1ng-001|Which atom or iron has the lowest ionization energy-- a hydrogen in the excited 2p state?

rCVJLXWD1ng-002|A helium plus in the excited 3p state?

rCVJLXWD1ng-003|Or lithium plus 2 in the excited 4p state?

rCVJLXWD1ng-010|We're talking about three species, and we're trying to determine the ionization energy.

rCVJLXWD1ng-013|So let's just do that.

rCVJLXWD1ng-014|For hydrogen in the 2p state, z is 1, charge in the nucleus, n is 2, so we'll have a quarter of a Rydberg to ionize.

rCVJLXWD1ng-017|We have 9/16 of a Rydberg, a little more than half a Rydberg to ionize.

luB5a39kGkA-000|Particles can have wave-like properties.

luB5a39kGkA-001|If the momentum is small enough, a moving particle displays the properties of a wave.

luB5a39kGkA-002|We can actually demonstrate it.

luB5a39kGkA-005|So electrons that behave like waves plus boundaries gives you quantization.

luB5a39kGkA-006|Now we need to look at that in an interesting situation.

luB5a39kGkA-007|We've looked at a particle in a one-dimensional box.

luB5a39kGkA-008|What about an atom?

luB5a39kGkA-009|An atom is an electron bound by the nucleus.

luB5a39kGkA-010|An electric charge holds the electron about the nucleus.

luB5a39kGkA-011|So that's a particle that behaves like a wave, plus boundaries on where it has to be in space.

luB5a39kGkA-012|That should lead to quantized energy levels for the electron.

luB5a39kGkA-013|So let's look at that carefully.

luB5a39kGkA-014|First, we'll have to describe three-dimensional space in terms of easy parameters for quantum mechanical calculations.

luB5a39kGkA-015|We'll do that using something called spherical polar coordinates.

luB5a39kGkA-018|So we'll get regions of space, just like in the particle in a box, where the particle is more likely to be located.

luB5a39kGkA-019|So let's look at these spherical polar coordinates.

luB5a39kGkA-020|How do we describe where an electron is about an atom?

luB5a39kGkA-021|Well, it's somewhere about the nucleus in three-dimensional space.

luB5a39kGkA-022|We'll draw a vector from the center of the coordinate system, which is where the nucleus will be, out to the electron.

luB5a39kGkA-023|And it'll have length r.

luB5a39kGkA-024|That will be our first coordinate, the length r.

luB5a39kGkA-025|Then we'll take the angle from the positive z-axis out to that vector r.

luB5a39kGkA-026|That will be the angle theta.

luB5a39kGkA-027|That's our second coordinate.

luB5a39kGkA-028|And then we'll take a third coordinate, the angle of the projection into the xy plane of the vector, and that'll be our third coordinate, phi.

luB5a39kGkA-029|So r, theta, phi.

luB5a39kGkA-030|Three coordinates for three dimensions of space.

luB5a39kGkA-033|For three dimensions, we'll get three quantum numbers, one for each dimension.

luB5a39kGkA-034|So those quantum numbers will be n, l, and m sub l.

luB5a39kGkA-035|Let's look at those quantum numbers and how they relate to the properties of the wave function.

luB5a39kGkA-036|So we'll look at the quantum number values and the orbital property.

luB5a39kGkA-037|Now I'm going to start to use the term orbital.

luB5a39kGkA-038|What I mean is wave function, or square of the wave function.

luB5a39kGkA-039|The orbital is the region in space where the electron can exist.

luB5a39kGkA-040|So that's what the wave function describes.

luB5a39kGkA-041|I'll use those two terms interchangeably.

luB5a39kGkA-042|So quantum number.

luB5a39kGkA-043|First, the principle quantum number, n, just like in a particle in a box, has values 1, 2, 3, and describes the overall energy of the system.

luB5a39kGkA-044|And just like in the particle in a box, when you have the total number of nodes, n minus 1, you know how high your energy is.

luB5a39kGkA-045|More nodes, more energy.

luB5a39kGkA-046|Now-- or a higher energy system.

luB5a39kGkA-047|Now remember node.

luB5a39kGkA-048|That's an area where the wave function goes to zero.

luB5a39kGkA-049|The square of the wave function is zero.

luB5a39kGkA-052|So the larger n, the more values of l you have.

luB5a39kGkA-053|So l starts at zero.

luB5a39kGkA-054|Now it's our first zero value quantum number.

luB5a39kGkA-055|And it counts up in integers up to n minus 1.

luB5a39kGkA-056|So if n is 3, l could be 0, 1, or 2.

luB5a39kGkA-057|That's n minus 1.

luB5a39kGkA-058|Now for l, we'll also use letter designations.

luB5a39kGkA-059|Now I know sometimes in chemistry you're thinking, you're throwing this nomenclature at me just to make it confusing.

luB5a39kGkA-060|And unfortunately for the s, p, and d designations, I don't have a good answer for you.

luB5a39kGkA-061|They're historical designations of these values of l, and you just have to memorize them.

luB5a39kGkA-062|It is kind of almost a confusion factor that we're going to throw in on top of this.

luB5a39kGkA-063|Sometimes the quantum numbers will be a number, and sometimes it's going to be a letter.

luB5a39kGkA-064|So memorize these values for l.

luB5a39kGkA-065|L tells you the overall shape of the orbital, the shape of the wave function.

luB5a39kGkA-066|Is it dumbbell shaped?

luB5a39kGkA-067|Is it spherical shape?

luB5a39kGkA-068|Is it elongated?

luB5a39kGkA-069|Is it narrow?

luB5a39kGkA-070|Those kind of things come from l.

luB5a39kGkA-072|And it will have values ranging from minus l to l.

luB5a39kGkA-073|So if l is 2, you'll go minus 2, minus 1, 0, 1, 2.

luB5a39kGkA-074|From minus l to l in integer steps.

luB5a39kGkA-075|So there could be many values of m sub l for a given value of l.

luB5a39kGkA-076|And it's going to tell you something about the orientation.

luB5a39kGkA-077|If I have a dumbbell shaped, maybe along the x-axis, maybe I'm along the z-axis.

luB5a39kGkA-078|M sub l will help you determine that.

luB5a39kGkA-079|So we're not going to look at the actual values of the wave function, the mathematical formulas.

luB5a39kGkA-080|What we will look at is the values of the quantum numbers.

luB5a39kGkA-081|Each set of quantum numbers describes an individual wave function.

luB5a39kGkA-082|Just like in a particle in a box when you took n equal 1, that was a single hump function.