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: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | so the length of this line right over here . that would be the radius . and so a lot of people when they conceptualize an atom they imagine a positive nucleus with the protons in the center right over here then they imagine the electrons on these fixed orbits around that nucleus so they might imagine some electrons in ... | what about ionic radius trends ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | so you 're adding more and more and more shells . here you have just the first shell , now the second shell and each shell is getting further and further and further away . so as you go down the periodic table , you are getting , you are getting larger . | our teacher said that neon has a larger atomic radius than lithium because the last shell is filled and so , the repulsion of electrons in the shell makes it slightly bigger than the lithium atom ... .. is it true ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | so that 'd be 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . so one way to think about it , if you have more positive charge in the center , and you have more negative charge on that outer shell , so that 's going to bring that outer shell inward . it 's going to have more i guess you could imagine one way , more coulomb attraction r... | based on other videos , does more electrons in outer shell equals lesser screening effect ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | : let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . | in the existence of elements with atomic numbers greater than 118 possible ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | well , as we go down a group , each new element down the group , we 're adding , we 're in a new period . we 're adding a new shell . so you 're adding more and more and more shells . | if an extension is possible where do you think should the new elements be placed ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | so the length of this line right over here . that would be the radius . and so a lot of people when they conceptualize an atom they imagine a positive nucleus with the protons in the center right over here then they imagine the electrons on these fixed orbits around that nucleus so they might imagine some electrons in ... | isnt kr 's radius more than k ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | : let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . | what is the shielding effect ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | so a covalent bond , we 've already- we 've seen this in the past . the most famous of covalent bonds is well , a covalent bond you essentially have 2 atoms . so that 's the nucleus of one . | sal says atooms are joined by covalent bonds ... ... so my first question is what are covalent bonds and how can we find radius if atom is not joined to anyone ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | so the length of this line right over here . that would be the radius . and so a lot of people when they conceptualize an atom they imagine a positive nucleus with the protons in the center right over here then they imagine the electrons on these fixed orbits around that nucleus so they might imagine some electrons in ... | for noble gases shouldnt i consider vanderwalls radius ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | : let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | i thought i understood the concept but why is potassium bigger than strontium even though strontium is on the fifth energy level ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | what do you think is going to be the trend here ? and if you want to think about the extremes , how do you think potassium is going to compare to krypton in terms of atomic radius . i encourage you to pause this video and think about that on your own . | what if i want to compare the atomic radius between boron and rubidium ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | you have 36 . you have a positive charge of 36 . let me write that , you have plus 36 . | when you say coulomb charge can it also be called nuclear charge/attraction ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | the most famous of covalent bonds is well , a covalent bond you essentially have 2 atoms . so that 's the nucleus of one . that 's the nucleus of the other . | if the coulomb force is attracting the electrons toward the nucleus , why does n't the atom just collapse into the nucleus ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | that 's the nucleus of the other . and they 're sharing electrons . so their electron clouds actually , their electron clouds actually overlap with each other , actually overlap with each other so the covalent bond , there the electrons in that bond could spend some of their time on this atom and some of their time on ... | sal said that the electrons are not in orbits , so it ca n't be centrifugal force that is keeping the electrons out of the nucleus , so what is it ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | so , you might have an orbital , and i 'm just showing you in 2 dimensions . it would actually be in 3 dimensions , where maybe there 's a high probability that the electrons where i 'm drawing it in kind of this more shaded in green . but there 's some probability that the electrons are in this area right over here an... | why does magnesium has high ionization energy.. ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | : let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . | why did sal go diagonally also to explain the atomic radius trends ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | well if you get larger as you go down , that means you 're getting smaller as you go up . you get smaller , smaller as you go up . so , what are going to be , what 's going to be the smallest ones ? | so , why would the atom get smaller when you go to the right ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | you have 36 . you have a positive charge of 36 . let me write that , you have plus 36 . | would n't there be more electrons to counteract the positive charge made by the protons ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | so you have 8 in your outermost shell . so that 'd be 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . so one way to think about it , if you have more positive charge in the center , and you have more negative charge on that outer shell , so that 's going to bring that outer shell inward . | 0 why does the outside have a negative attraction than the other orbitals ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | that 's the nucleus of the other . and they 're sharing electrons . so their electron clouds actually , their electron clouds actually overlap with each other , actually overlap with each other so the covalent bond , there the electrons in that bond could spend some of their time on this atom and some of their time on ... | likewise , how would the outermost electrons be attracted to the nucleus because of such a distance and the inner shells of electrons ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | so the length of this line right over here . that would be the radius . and so a lot of people when they conceptualize an atom they imagine a positive nucleus with the protons in the center right over here then they imagine the electrons on these fixed orbits around that nucleus so they might imagine some electrons in ... | would n't the distance and repulsion of the other electrons prevent a strong attraction ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | well if you get larger as you go down , that means you 're getting smaller as you go up . you get smaller , smaller as you go up . so , what are going to be , what 's going to be the smallest ones ? | so , is hydrogen atom smaller than zenon ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | : let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . | how is the atomic radius of a particular atom of an element determined ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | : let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . | what exactly is atomic radius ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | so these are all different ways of thinking about it . now , with that out of the way , let 's think about what the trends for atomic size or atomic radii would be in the periodic table . so the first thing to think about is what do you think will be the trend for atomic radii as we move through a period . | discuss atomic radius trend in the periodic table ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | now what do you think is going to happen as we go down the period table ? as we go down the periodic table in a given group ? well , as we go down a group , each new element down the group , we 're adding , we 're in a new period . | the largest atom in periodic table ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | : let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . | just to be clear , does ionic and atomic radius increases from left to right and also increase from bottom to top ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | a cycle would look like this whole process right there . so recapping : the amplitude of a simple harmonic oscillator is the maximum magnitude of displacement from the equilibrium position . you can measure it that way or you can measure it this way , you would get the same amount . | does amplitude and period of simple harmonic motion affect each other ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | repeat a whole cycle , eh ? alright i 'm gon na go from this equilibrium position back to that equilibrium position . that 's not a whole cycle . | so if the spring is pulled a farther distance from the equilibrium position does the period get affected ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | and this is great ! 'cause now we can draw the variables we talked about earlier like amplitude , because amplitude is the maximum magnitude of displacement from equilibrium . that would equal point two meters . | is like valley is the amplitude ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | if we put that in meters , technically si units , you should have meters for the default units , so this would be point two . zero point two meters , and that 's also the amplitude . so remember , this is the amplitude . so this distance here is the amplitude . | what is the unit of amplitude ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | now , this is getting kind of messy . and honestly , for that reason people often draw what the simple harmonic oscillator looks like on a graph . it turns out to be particularly elegant and useful to represent these ideas on a graph . | should n't this be easier if we explained simple harmonic oscillations with the trigonometric circle and pi 's ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | repeat a whole cycle , eh ? alright i 'm gon na go from this equilibrium position back to that equilibrium position . that 's not a whole cycle . | 2 , should n't the object go back to its equilibrium position after the spring is extended and then let go , instead of compressing the spring again ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | so we are essentially graphing what this is . this is x . the horizontal position has a function of time . | another guess is how if the oscillator behave as sin^2 x ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | but long ago physicists decided : you know what ? time , if time is involved , we are sticking that bad boy on the horizontal axis . this is just designated . | if a body covers one complete vibration in time t then at what point will the body be present at time t/8 ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | it will be given in seconds , so for the sake to making this a little less abstract , let 's say for example , the period of this mass on the spring was six seconds . what would that mean ? it would mean that it took six seconds for the mass to go from this point and then all the way back to that point resetting itself... | will it be present between mean positon and extreme position or somewhere else ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | it goes through that point and comes back , so essentially what you 're gon na have on here goes toward equilibrium , so it looks like this , goes toward equilibrium , boom ! hits equilibrium . and that 's when it 's at x equals zero . | what will happen to velocity at equilibrium point ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | if we want to , we can just say this amplitude here . this would also be the amplitude , because we 're just talking about the maximum magnitude of displacement . so it 's gon na get displaced equally on either side of the equilibrium position and that maximum amount is called the amplitude . | - if amplitude is the madnitude of displacement why would it always be positive ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | right ? magnitude of the displacement . so it 's the magnitude of the vector , so it 's always positive . | why do n't we say maximum distance instead magnitude of displacement ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | you could have measured it from , sometimes people call these troughs or valleys , so you can measure it trough to trough , or valley to valley , took three seconds to nine seconds . that 's a time of six seconds . it took six seconds to go from three seconds to nine seconds . that 's still one whole period . | why is the 20cm placed at zero seconds and not at 1 second ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | repeat a whole cycle , eh ? alright i 'm gon na go from this equilibrium position back to that equilibrium position . that 's not a whole cycle . | can we treat the period as the time taken for a body to oscillate from equilibrium position to extreme position , then back to the other extreme , and then back to mean ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | so that 's kinda ugly looking . it 's better to represent this on a graph . what would that look like ? | beginning why does david graph the oscillation as a cosine wave , and not a sine wave ? |
alright so there 's some terminology you got ta get used to when dealing with simple harmonic oscillators because people and books and teachers and professors are gon na throw these terms around like crazy , and if you are not used to them , it all can sound like mathematical witchcraft . so the first term you got ta ... | the mass has been stopped by this spring . and it 's gon na come back up and this process is gon na repeat , it 's gon na go back through the equilibrium position and come back up . which by up it means over here back to this initial point . that 's one whole cycle . | therefore , should not the graph start at 0 , rise in the first quadrant according to the distance the weight is first pulled , and then proceed with the negative movement of it bouncing back ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . | - what is the second condition given for ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | so based on that , this thing right over here is always greater than or equal to zero . the limit as one over n or as our b sub n , as n approaches infinity is going to be zero , it 's a decreasing sequence . therefore we can say that our original series actually converges . | is n't it clear , that if lim ( b_n ) = 0 when n - > infinity , then { b_n } should be decreasing sequence only ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | so for all of these integer n 's greater than or equal to k. so if all of these things are true , and we know two more things . and we know number one , the limit as n approaches infinity of b sub n is equal to zero . and number two , b sub n is a decreasing sequence . | how this sequence could be not decreasing if the limit of b_n ( when n - > infinity ) is equal zero ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | and we know number one , the limit as n approaches infinity of b sub n is equal to zero . and number two , b sub n is a decreasing sequence . then that lets us know that the original infinite series is going to converge . | do n't the first two rules imply the third ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | so let 's say that i have some series , some infinite series . let 's say it goes from n equals k to infinity of a sub n. let 's say i can write it as , or i can rewrite a sub n. so a sub n is equal to negative one to the n , times b sub n , or a sub n is equal to negative one to the n plus one , times b sub n , where ... | what about ( -1 ) ^ ( n+2 ) , ( -1 ) ^ ( n^2 ) , or any polynomial exponent with odd integer coefficients ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | if the limit of your terms do not approach zero , then you say okay , that thing is going to diverge . this thing is useful because you can actually prove convergence . now once again , if something does not pass the alternating series test , that does not necessarily mean that it diverges , it just means that you coul... | can you use the alternating series test to prove divergence ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | so we satisfy the first constraint . and then , this is clearly a decreasing sequence . as n increases , the denominators are going to increase , and with a larger denominator you 're going to have a lower value . | what is the sum of the sequence shown in the lesson ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . | is it the rule2 ( { bn } dicreasing seq ) necessary ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | so our b sub n is equal to one over n. now clearly this is going to be greater than or equal to zero for any positive n. now what 's the limit ? what 's the limit of b sub n as n approaches infinity ? the limit of one over n as n approaches infinity is going to be equal to zero . | if the limit as n aproaches infinity is 0 is the series not always decreasing ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | is it true that b sub n must be positive for alternating series test to work ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | i mean why is this convergent while the positive harmonic series diverges ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | so for all of these integer n 's greater than or equal to k. so if all of these things are true , and we know two more things . and we know number one , the limit as n approaches infinity of b sub n is equal to zero . and number two , b sub n is a decreasing sequence . | sal specifies that one of the conditions for the alternating series to converge is that the limit as n- > infinity of b_n = 0 , though would n't it be sufficient to know that the limit is less than 1 , as in the ratio test ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . | what is the intuition/proof of this fact ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | why is it that the harmonic series diverges , but the alternating harmonic series converges ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | how is the limit 0 for a divergent series ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | so based on that , this thing right over here is always greater than or equal to zero . the limit as one over n or as our b sub n , as n approaches infinity is going to be zero , it 's a decreasing sequence . therefore we can say that our original series actually converges . | if the limit of bn do n't equal to zero or not decreasing sequence does this test tell us that the series will be surely diverge ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | so we satisfy the first constraint . and then , this is clearly a decreasing sequence . as n increases , the denominators are going to increase , and with a larger denominator you 're going to have a lower value . | what does decreasing sequence mean ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | let 's use this with an actual series to make it a little bit more concrete . so let 's say that i had the series from n equals one to infinity of negative one to the n over n. and we can write it out just to make this series a little bit more concrete . when n is equal to one , this is going to be negative one to the ... | can we then say that the series is convergent for n > no and by following one of the series properties ( adding or substracting definite number of an seriess convergence does n't change ) state that the series is convergent given any n ? |
let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | let 's now expose ourselves to another test of conversions , and that 's the alternating series test . and i 'll explain the alternating series test , and i 'll apply it to an actual series while i do it to make the explanation of the alternating series test a little bit more concrete . so let 's say that i have some ... | how do you apply nth term to alternating if both alternating and ratio test are inconclusive ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | and according to the uncertainty principle , you ca n't know the position and momentum of that particle accurately , at the same time . so if you know the position , if you know where that particle is in space really well , you do n't know the momentum , or you do n't know the velocity of that particle , and vice versa... | how do we know the uncertainty in the velocity of the particle ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | - heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | jay said if we know the position of particle in space we cant find out momentum of that particle my question is why we cant find out the momentum of that particle if we know the position ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | and the units would be , this is the mass in kilograms , and the velocity was in meters over seconds , so kilograms times meters per second . alright , so this is the uncertainty associated with the momentum of our electrons . let 's plug it in to our uncertainty principle here : we had the uncertainty in the position ... | suppose we can measure the velocity without any uncertainty in future , will it be appropriate to treat electrons as only particles ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | alright , so this is the uncertainty associated with the momentum of our electrons . let 's plug it in to our uncertainty principle here : we had the uncertainty in the position of the electron , times the uncertainty in the momentum of the electron must be greater than or equal to planck 's constant divided by four pi... | because , if i have a detector , and emit an electron ... and the electron hits position x1 at time 1 , then position x2 at time 2 , then i have a history of the electron without any uncertainty in either momentum or position , right ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | let 's say we knew the velocity with a 10 % uncertainty associated with that number . so a 10 % uncertainty . if we convert that to a decimal , we just divide 10 by 100 , so we get 10 % is equal to point one . | 6 , why do we multiply the equation by .1 when there is a 10 % uncertainty ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | so the uncertainty in the position , so delta x is the uncertainty in the position , times the uncertainty in the momentum , so delta p is uncertainty in momentum , the product of these two must be greater than or equal to some constant . and that constant is planck 's constant : h divided by four pi . so we have a con... | how was planck 's constant formed ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | - heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | why can not we , in general , figure out the velocity and position of a particle simultaneously ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | - heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . | can someone explain it in terms of radiations and wavelength ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you ca n't know the position and momentum of that particle accurately , at the... | but what does it mean for there to be an uncertainty in time of a particle vs it 's energy ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | if you know the momentum really well , you do n't know the position . so let 's look at a mathematical description of the uncertainty principle . so the uncertainty in the position , so delta x is the uncertainty in the position , times the uncertainty in the momentum , so delta p is uncertainty in momentum , the produ... | for the heisenburg uncertainty principle , where did the 4 pi come from in the equation , which is `` x times p is greater than or equal to h divided from 4 pi '' ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | let 's say we knew the velocity with a 10 % uncertainty associated with that number . so a 10 % uncertainty . if we convert that to a decimal , we just divide 10 by 100 , so we get 10 % is equal to point one . | what does an uncertainty of 2 mean ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | let 's say we knew the velocity with a 10 % uncertainty associated with that number . so a 10 % uncertainty . if we convert that to a decimal , we just divide 10 by 100 , so we get 10 % is equal to point one . | does it mean on a scale of 1 to 10 , my uncertainty is rated 2 ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | - heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | why can not we determine the position and momentum of the particle at the same time ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | let 's say we knew the velocity with a 10 % uncertainty associated with that number . so a 10 % uncertainty . if we convert that to a decimal , we just divide 10 by 100 , so we get 10 % is equal to point one . | how can uncertainty be measured ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | so we could solve for the uncertainty in the position . so , delta x must be greater than or equal to , let 's go ahead and do that math . so we have planck 's constant , 6.626 times 10 to the negative 34 , we divide that by 4 , we need to divide that also by pi , and then we need to divide by the uncertainty in the mo... | how do we know delta x delta p is constant ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | - heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . | why does physics have to be so complicated ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | this product must be greater than or equal to , planck 's constant is 6.626 times 10 to the negative 34 . alright , divide that by four pi . so we could solve for the uncertainty in the position . | 0 , where does that 4 pi come from ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | let 's say we knew the velocity with a 10 % uncertainty associated with that number . so a 10 % uncertainty . if we convert that to a decimal , we just divide 10 by 100 , so we get 10 % is equal to point one . | what does 10 % uncertainty mean ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | and , let 's say the electron is going this direction , so there is a velocity associated with that electron , so there is velocity going in that direction . alright , the reason why the bohr model is useful , is because it allows us to understand things like quantized energy levels . and we talked about the radius for... | are shells and energy levels the same ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | let 's say we knew the velocity with a 10 % uncertainty associated with that number . so a 10 % uncertainty . if we convert that to a decimal , we just divide 10 by 100 , so we get 10 % is equal to point one . | what does uncertainty of 2 means ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | so the uncertainty in the position must be greater than or equal to 2.6 times 10 to the negative 10 and if you worked our your units , you would get meters for this . so the uncertainty in the position must be greater than or equal to 2.6 times 10 to the negative 10 meters . let 's go back up here to the picture of the... | its speed can be measured with precision 1 % .its uncertainity in position is equal to of greater than ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | so let 's look at a picture of the bohr model of the hydrogen atom . alright , we know our negatively charged electron orbits the nucleus , like a planet around the sun . and , let 's say the electron is going this direction , so there is a velocity associated with that electron , so there is velocity going in that dir... | is there any model that gives us more certainty regarding postion and momentum of an electron around the nucleus ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | alright , divide that by four pi . so we could solve for the uncertainty in the position . so , delta x must be greater than or equal to , let 's go ahead and do that math . | but if there were a past-future symmetry ( both retarded and advanced waves as feynmann and wheeler , einstien in a paper in 1909 and a few other physicists ) then we could not be entirely sure of the past either ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | - heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . | is there any proof of the heisenberg 's uncertainty principle ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | the uncertainty principle says this is n't true . if we know the velocity fairly accurately , we do n't know the position of the electron , the position of the electron is greater than the diameter , according to the bohr model . so this just one reason why the bohr model is wrong . | how did heisunburg prove that the position of electron can not be determined excatly ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | so the uncertainty in the position , so delta x is the uncertainty in the position , times the uncertainty in the momentum , so delta p is uncertainty in momentum , the product of these two must be greater than or equal to some constant . and that constant is planck 's constant : h divided by four pi . so we have a con... | why is plank 's constant used in the equation ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | so the uncertainty in the position , so delta x is the uncertainty in the position , times the uncertainty in the momentum , so delta p is uncertainty in momentum , the product of these two must be greater than or equal to some constant . and that constant is planck 's constant : h divided by four pi . so we have a con... | why not some other constant like pi or speed of light ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | it 's telling us we know the electron is orbiting the nucleus at a certain radius , and it 's moving at a certain velocity . the uncertainty principle says this is n't true . if we know the velocity fairly accurately , we do n't know the position of the electron , the position of the electron is greater than the diamet... | how can you prove that the formula for the uncertainty principle is true ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | - heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . | how can one be so certain that the uncertainty principle is very accurate ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | so the uncertainty in the position , so delta x is the uncertainty in the position , times the uncertainty in the momentum , so delta p is uncertainty in momentum , the product of these two must be greater than or equal to some constant . and that constant is planck 's constant : h divided by four pi . so we have a con... | how was the planck 's constant found ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | so if two times two is equal to four . if i decrease the uncertainty of the position , so i decrease it to one , so the uncertainty in the momentum must increase to four , because one times four is equal to four . if i decrease the uncertainty in the position even more , so if i lower that to point five , i increase th... | what happens if we decrease the uncertainty of either the momentum or position to 0 ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | let 's say we knew the velocity with a 10 % uncertainty associated with that number . so a 10 % uncertainty . if we convert that to a decimal , we just divide 10 by 100 , so we get 10 % is equal to point one . | how does one find the minimum uncertainty for an photon considering it has no mass ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | alright , divide that by four pi . so we could solve for the uncertainty in the position . so , delta x must be greater than or equal to , let 's go ahead and do that math . | what happens when uncertainty in position = 0 ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | alright , divide that by four pi . so we could solve for the uncertainty in the position . so , delta x must be greater than or equal to , let 's go ahead and do that math . | what does uncertainty in position mean ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | so we have planck 's constant , 6.626 times 10 to the negative 34 , we divide that by 4 , we need to divide that also by pi , and then we need to divide by the uncertainty in the momentum . so we also need to divide by the uncertainty in momentum , that 's 2.0 times 10 to the negative 25 , and that gives us 2.6 times 1... | when he said uncertainity of the position of electron deltax is > = 2.6 x 10^-10 does that mean that certainity of finding the electron is more in the radius lesser than 2.6 x 10^-10 ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | so let 's look at a picture of the bohr model of the hydrogen atom . alright , we know our negatively charged electron orbits the nucleus , like a planet around the sun . and , let 's say the electron is going this direction , so there is a velocity associated with that electron , so there is velocity going in that dir... | since a node is a region of space where it would be impossible to find an electron , does that mean that it represents the positively charged nuclear core in an atom ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | let 's say we knew the velocity with a 10 % uncertainty associated with that number . so a 10 % uncertainty . if we convert that to a decimal , we just divide 10 by 100 , so we get 10 % is equal to point one . | what exactly does an uncertainty percentage signify ? |
- heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | - heisenberg uncertainty principle is a principle of quantum mechanics . and so if we take a particle , let 's say we have a particle here of mass m , moving with velocity v , the momentum of that particle , the linear momentum is equal to the mass times the velocity . and according to the uncertainty principle , you c... | if we reduce the uncertainty of the position of the particle to 0 , what will we know about the momentum of the particle ? |
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