Question

Calculate a value of effective magnetic moment `mu_(eff)` of `Ce^(3+)` ion.

Answer 1

`mu_(eff) = g sqrt(J(J+1))` ....(i)
where `g = 1 + [(S(S+1)-L(L+1)+J(J+1))/(2J(J+1))]` ...(ii)
`Ce^(3+)` as `f^(1)` configuration
`:. S = 1 xx (1)/(2) = (1)/(2)`
`L = 3`
`J =L - S`
(Subshell is less than half-filled)
`= 3-(1)/(2) = (5)/(2)`
from (ii)
`g = 1 + ([((1)/(2) xx (3)/(2))-(3 xx 4)+((5)/(2) xx (7)/(2))])/(2 xx (5)/(2) xx (7)/(2))= (6)/(7)`
from (i)
`mu_(eff) = gsqrt(J(J+1))BM`
`= (6)/(7) sqrt((5)/(2) xx (7)/(2)) = 2.54 BM`