Consider the following sets of quantum numbers: array|c|c|c|c|c| & n & l & m & s \ (i) & 3 & 0 & 0 & +1/2 \ (ii) & 2 & 2 & 1 & +1/2 \ (iii) & 4 & 3 & -2 & -1/2 \ (iv) & 1 & 0 & -1 & -1/2 \ (v) & 3 & 2 & 3 & +1/2 \ array Which of the following sets of quantum numbers are not possible?
- (i), (ii), (iii) and (iv)
- (ii), (iv) and (v)
- (i) and (iii)
- (ii), (iii) and (iv)
Answer
(2) (ii), (iv) and (v)
Solution
Rules: l = 0, 1, , (n-1); m = -l, , 0, , +l; s = 12
(i) n=3, l=0, m=0 ⇒ possible (3s)
(ii) n=2, l=2 ⇒ not possible, ∵ l can be at most n-1 = 1
(iii) n=4, l=3, m=-2 ⇒ possible (4f)
(iv) n=1, l=0, m=-1 ⇒ not possible, ∵ for l=0, m=0 only
(v) n=3, l=2, m=3 ⇒ not possible, ∵ for l=2, m ranges from -2 to +2
∴ Sets (ii), (iv) and (v) are not possible.
Answer: (2)