Finding total angular momentum qnumber for 3d4d

[linda300]

Hey,

I've been able to do most of these problems but at this point I stopped because it gives 5 values for L and I just wanted to double check it is correct.

L = 2+2,...,2-2 = 4,3,2,1,0

S = 1,0

then you have to evaluate J for each L and S which will give 10 possibilities.

It's a pretty small question but, is it ok to have 5 values for L?

 

[I like Serena]

Hi linda300!

Can you provide some more information?

What do you mean by a "qnumber"?
What do you mean by "3d4d"?
What do you mean by an L-number? Do you mean an angular momentum?
What do you mean by an S-number?
What do you mean by J?

I guess I didn't learn from the same book you're doing now and I may be used to different symbols and definitions.
I'll adjust to the symbols you are using, but I will need their definitions.

 

[linda300]

oh sorry,

i've read a few books which used wither L or l' notation for angular momentum,

qnumber i meant quantum number but i thought it might not fit in the heading,

3d4d means one electron at n=3, l=2 and one at n=4,l=2

S total spin= s₁+s₂, s₁+s₂-1,...,|s₁-s₂|

J total angular momentum= L+S, L+S-1,...,|L-S|

I think it's fine to have 10 different combinations they all look good,

However I do have another question related to this,

Spectroscopic notation is ^2S+1X_J
Where X is the angular momentum according to below
If X= S, P, D, F, G, H...
Then L= 0 , 1, 2, 3, 4, 5...

Take ⁵P₀ for example. so S=2, L=1 and J = 0

But according to S=2, L=1, J=3,2,1. so this state is impossible right? Also consider ³D₁ S=1, L=2, J=1 which is possible,

Since S=1 does this mean that there must be 2 optically active electrons?

I think that's right but i just wanted to double check,

Thanks for answering