Question

Consider the following sets of quantum number:

	n	l	m	s
(a)	3	0	0	${+}^{1/2}$
(b)	2	2	1	${+}^{1/2}$
(c)	4	3	-2	${-}^{1/2}$
(d)	1	0	-1	${-}^{1/2}$
(e)	3	2	3	${+}^{1/2}$

Which of the following sets of quantum number is not possible:

• A. a and c
• B. b, c and d
• C. a, b, c and d
• D. b, d, and e

Answer 1

The correct option is D b, d, and e

For any value of $n$, possible values of $l$ are $0$ to $n-1$ and for each $l$ possible values of $m_l$ are $-lto0$ to $+l$ and possible values of $m_s$ is $+1/2$or $-1/2$

for given $n$ allowed values of other quantum numbers are:

(a)$n=3;l=0,1,2;m_l=-2,-1,0,1,2;m_s=+1/2or-1/2$:

(b) $n=2,l=0,1;m_l=-1,0,1;m_s=+1/2or-1/2$

(c) $n=4,l=0,1,2,3;m_l=-3,-2,-1,0,1,2,3;m_s=+1/2or-1/2$

(d) $n=1,l=0;m_l=0;m_s=+1/2or-1/2$

(e) $n=3,l=0,1,2;m_l=-2,-1,0,1,2;m_s=+1/2or-1/2$

therefore (b), (d), (e) are incorrect set of quantum numbers.

option D is correct