Electron Configuration

[dcm18]

Can anyone tell me how I can determine the allowed quantum numbers, ml and ms, and the max occupancy of sub shells for lets say 5g.......

 

How can I determine the ground-state term symbols for lets say p^4 or d^5....

 

And finally how do i figure out the term symbols for ground-state configurations of the atoms H thru F?

 

Any direction would be much appreciated....

 

Thanks

[Riogho]

Look up Noble Gas Configuration

[Testo]

For determining quantum numbers;

 

n = 1,2,3,4...

l = 0,1,2,3...(n-1)

ml = 0, +/-1, +/-2, +/-3...+/-l

ms = +/-0.5

 

So for 5g, n=5 and l=4 (0=s, 1=p, 2=d etc.) so ml values can be -4 up to +4 (nine orbitals) each with 2 electrons with +0.5 and -0.5, max occupancy is 18 electrons

 

Term symbols are more tricky; the letter represents the orbital quantum number l, the left superscript is the spin multiplicity = 2s+1 where s is the total spin angular momentum quantum number. A single electron has an s of 0.5 so 2(0.5)+1 = 2. Two electrons has two combinations S = 0, 1 (0.5+0.5=1, 0.5-0.5=0) which gives Either 1 (singlet state) or 3 (triplet state) spin multiplicities and so on.... The right subscript is the total angular quantum number J = L+S, L+S-1, ... |L-S|

 

The best way to show this is an example e.g. H 1s^1;

s=0.5 => 2s+1 = 2

l=0 => S

J= 0+0.5 = 0.5

 

For He 1s^2

s=0, 1 => 2s+1 = 1 AND 3

l=0 => S

J= 0+0 = 0 AND 0+1 = 1

So helium has a triplet S and a singlet S state