Answer only two of questions a) to f) below. Each question is worth 10 points, i
ID: 527229 • Letter: A
Question
Answer only two of questions a) to f) below. Each question is worth 10 points, if you answer mor three, cross the answers you don't want graded. Otherwise only the first three answered will be graded. a) Derive the ground state term symbol of scandium. b) How many microstates are there in the term^4P (i.e.: what is its total degeneracy?) c) The principal line in the emission spectrum of sodium is yellow. Upon close inspection, the line is set doublet with wavelengths of 589.0 and 589 6 nm. Explain the origin of this doublet d) Is phi(1, 2) = 1s(1) a(1)1s(2)a(2) + 1s(2) a(2)1s(1) a(1) an eigenfunction of the operator Sz? Is so, what is value of M_L?Explanation / Answer
a)Electron configuration of Sc is [Ar]3d1 4s2
term symbol is defined as (2S+1)LJ
where S=total spin number
(2S+1) =multiplicity
J=total angular moment
L=sum of magnetic moments
3d1
S=1/2(only one electron)
5 d orbitals with magnetic moment values 2,1,0,-1,-2 as only one electron occupies the highest one l1=2
L=2 (D)
So J=L+S=2+1/2=3/2
2S+1=2*1/2+1=2
term symbol -2D3/2 for ground state or d1
b)total number of microstates is given by (2L+1)(2S+1)
4P
L=1(P)
S=3/2
So total number of microstates is given by (2L+1)(2S+1)
(2*1+1)(4)=3*4=12 microstates
c)