Question

Which of the following set of quantum numbers is permissible?

• A. $4,1,+2,+\frac{1}{2}$
• B. $4,2,-1,+\frac{1}{2}$
• C. $4,0,0,1$
• D. $4,4,+2,-\frac{1}{2}$

Answer 1

The correct option is B $4,2,-1,+\frac{1}{2}$

We know that,
Principal quantum number $=n$
Azimuthal quantum number $=l$
where, $0\le l\le n-1$
Magnetic quantum number $=m$
where, $-l\le m\le l$
Spin quantum number $=s$
where, $s=-\frac{1}{2}$ or $+\frac{1}{2}$

Quantum numbers are given as $(n,l,m,s)$

In (a),
$n=4$, $l=1$, $m=+2$ and $s=+\frac{1}{2}$
$l$ ranges from $0$ to $3$
For $l=1$, $m=-1,0,+1$
$\because$ $m=+2$
Not permissible

In (b),
$n=4$, $l=2$, $m=-1$ and $s=+\frac{1}{2}$
$l$ ranges from $0$ to $3$
For $l=2$, $m=-2,-1,0,+1,+2$
$\because$ $m=-1$ and $s=+\frac{1}{2}$
Permissible

In (c),
$n=4$, $l=0$, $m=0$ and $s=1$
$l$ ranges from $0$ to $3$
For $l=0$, $m=0$
$\because$ $s$ can be either $+\frac{1}{2}$ or $-\frac{1}{2}$
Not permissible

In (d),
$n=4$, $l=4$, $m=+2$ and $s=-\frac{1}{2}$
$l$ ranges from $0$ to $3$
$\because l=n$
Hence it is not permissible