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Consider the following sets of quantum numbers:
(i) $n = 3$, $l = 0$, $m = 0$, $s = +\dfrac{1}{2}$
(ii) $n = 2$, $l = 2$, $m = 1$, $s = +\dfrac{1}{2}$
(iii) $n = 4$, $l = 3$, $m = -2$, $s = -\dfrac{1}{2}$
(iv) $n = 1$, $l = 0$, $m = -1$, $s = -\dfrac{1}{2}$
(v) $n = 3$, $l = 2$, $m = 3$, $s = +\dfrac{1}{2}$
Which of the following sets of quantum numbers is not possible?
(i) $n = 3$, $l = 0$, $m = 0$, $s = +\dfrac{1}{2}$
(ii) $n = 2$, $l = 2$, $m = 1$, $s = +\dfrac{1}{2}$
(iii) $n = 4$, $l = 3$, $m = -2$, $s = -\dfrac{1}{2}$
(iv) $n = 1$, $l = 0$, $m = -1$, $s = -\dfrac{1}{2}$
(v) $n = 3$, $l = 2$, $m = 3$, $s = +\dfrac{1}{2}$
Which of the following sets of quantum numbers is not possible?
A
(i), (ii), (iii) and (iv)
B
(ii), (iv) and (v)
C
(i) and (iii)
D
(ii), (iii) and (iv)
Detailed Solution
Rules: for a given $n$, $l$ varies from 0 to $(n - 1)$; for a given $l$, $m$ varies from $-l$ to $+l$; and $s = \pm\dfrac{1}{2}$.
(i) $n = 3$, $l = 0$, $m = 0$: allowed (3s orbital).
(ii) $n = 2$, $l = 2$: not possible, because for $n = 2$, $l$ can be only 0 or 1.
(iii) $n = 4$, $l = 3$, $m = -2$: allowed (4f orbital).
(iv) $n = 1$, $l = 0$, $m = -1$: not possible, because for $l = 0$, $m$ can be only 0.
(v) $n = 3$, $l = 2$, $m = 3$: not possible, because for $l = 2$, $m$ varies only from $-2$ to $+2$.
So the sets that are not possible are (ii), (iv) and (v).
(i) $n = 3$, $l = 0$, $m = 0$: allowed (3s orbital).
(ii) $n = 2$, $l = 2$: not possible, because for $n = 2$, $l$ can be only 0 or 1.
(iii) $n = 4$, $l = 3$, $m = -2$: allowed (4f orbital).
(iv) $n = 1$, $l = 0$, $m = -1$: not possible, because for $l = 0$, $m$ can be only 0.
(v) $n = 3$, $l = 2$, $m = 3$: not possible, because for $l = 2$, $m$ varies only from $-2$ to $+2$.
So the sets that are not possible are (ii), (iv) and (v).