Using Hund's rules to calculate ground state of erbium

[roberto85]

Homework Statement

Calculate ground state of erbium [Xe] 4f^12 6s^2

The Attempt at a Solution

so i know that the f orbital can hold 14 electrons and has 7 types of orbitals that is -3,-2,-1,0,1,2,3

So i constructed a table with axes of m_l (-3 to +3 above) and m_s. Then hunds rules say i first maximise spin and then orbital angular momentum. So i placed electrons in order to maximise spin and I am left with the ml=-3,-2 boxes with only one electron and all the other boxes are filled with 2. But I am not getting the same answer as the question gives. I must be doing this wrong, any help please. I am getting L = 5 and S = 1 but the answers are L=9 and S=3? Many thanks

Roberto

 

[roberto85]

I'm also stuck on the next part of this question which asks what happens to the ground state of erbium in a magnetic field. It says i require the lande g factor:

g = [3J(J+1) + S(S+1) + L(L+1)]/2J(J+1)

Using the answers of s=3, l=9 AND j=12 i get g equal to 1.25.

But the answers give the change in energy as -0.75 M_j mu_B B which i know is the equation where in place of the -0.75 is the landau g factor, but this doesn't agree with my calculated value. Have i missed something or is this a typo? The answer also says that the degenerate groundstate will split into 25 states, how is this so and how would i be expected to know this? Many thanks again

Roberto

p.s i think I've found the equation which i need which is: Change in energy = mu_B (M_L + g_s x M_S) B

how do i know the values of M_L and M_S? Also i read that this equation applies in the strong field limit but i don't understand how the question implies this instead of the wak limit, should i always assume the strong limit in questions unless stated? Apologies for so many questions but i really want to know how to do these types of questions. Thanks