0:00
Aloha.
00:01
So for this problem, we're going to be asking questions about the transition of an atom from a 2p state to a 1s state.
00:11
And we're told that when there's no magnetic field, there's a photon emitted for this transition with lambda is 122 nanometers.
00:22
And we're going from 2p to 1s.
00:26
And the first part of the problem, this is without b field, an external b field.
00:39
And then we're asked to consider what happens when we turn on external magnetic field, which is in the z direction.
00:55
We're more expensive.
00:56
We're just looking at orbital effects here with this magnetic field.
01:01
And we want to know the number of wavelengths, so the number of lambda values for the photons emitted for this transition when it's in the magnetic field.
01:14
So that's part of the problem.
01:18
I'm just calling them lambda as the different number of wavelengths for this transition in the external magnetic field.
01:31
And related question in part a is the ml values or the magnetic quantum number, values for the initial and final states associated with each of these lambas.
01:57
So first thing i would do is if you don't know spectroscopic notation very well, i would look up this in a table in the textbook.
02:06
Because that's what 2p and 1s are.
02:09
So the 2p state, this means that the principal quantum number is 2, and the orbital quantum number is in less than n minus 1.
02:26
So that means l is 1.
02:28
Or that's what the p, the p signifies that l is 1.
02:33
And then there is ml values.
02:37
The magnetic quantum number values can range from minus l to l.
02:41
So there's three ml values for the state, minus 1, 0, and 1.
02:46
So minus l to l.
02:48
And then for the 1s state, n is 1, the s state, n is 1, means l is 0.
02:56
And then if l is zero, ml can only be zero because ml ranges from minus l to l.
03:03
So this is more details about these two states.
03:07
And when we are told about this magnetic field, this external magnetic field coming on, this should make you think of the z -mond effect because this effect is the splitting of the atomic energy levels when the atom is in the magnetic field according to the ml values.
03:29
So we can draw an energy level diagram.
03:31
So just make this axis be energy and the x -axis or the horizontal axis doesn't really have any meaning.
03:38
And initially we have this transition going on.
03:47
So this will be the 2p state going down to the 1s state.
03:52
And maybe in a different color.
03:56
Draw some photon going away, which has the lambda 122 nanometers.
04:06
And then this is without an external b field.
04:18
And then we'll draw us again with a b field.
04:28
And instead of having just one to be state, we're going to have a splitting of the energy levels from the zmon effect.
04:37
So we'll still be going down to only one state, one final state, the one s state.
04:45
But here we have ml is 1.
04:50
Ml is 0 and ml is minus 1.
04:56
And there's going to be a transition to the 1st state from each of these split up levels...