Question

Consider the following sets of quantum numbers:

	n	l	m	s
(i)	3	0	0	$+\frac{1}{2}$
(ii)	2	2	1	$+\frac{1}{2}$
(iii)	4	3	2	$-\frac{1}{2}$
(iv)	1	0	1	$+\frac{1}{2}$

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

• A. (i), (ii), (iii) and (iv)
• B. (ii) and (iv)
• C. (i) and (iii)
• D. (i), (iii) and (iv)

Answer 1

The correct option is B (ii) and (iv)

We know,
'n' is the principal quantum number.
'l' is the azimuthal quantum number and it can take up any values from $0$ to $n-1$.
'm' is the magnetic quantum number and it can have any values from $-l$ to $+l$.
's' is the spin quantum number and its value can be either $+\frac{1}{2}$ or $-\frac{1}{2}$

Here in the (ii) set, $n=2$ and also $l=2$, which is not possible since the possible value of $l$ lies in the range 0 to $n-1$ only.

In the set (iv), $l=0$ and $m=1$, which is not possible since possible value of m lies in the range $-l$ to $+l$ only.

Therefore the (ii) and (iv) sets of quantum numbers are not possible.