Question

The maximum number of electrons that can have principal quantum number, $n=4$ and spin quantum number, $m_s=-\frac{1}{2}$ is:

• A. $8$
• B. $9$
• C. $16$
• D. $32$

Answer 1

The correct option is C $16$

For a shell with principal quantum number ${}^{\prime }{n}^{\prime }$, maximum number of electrons that can occupy the shell = $2n^2$
For $n=4$, maximum number of electrons = $2\times 4^2=32$
Half of them will have $m_s=-\frac{1}{2}$ and the other half will have $m_s=+\frac{1}{2}$ .
$\therefore$ Maximum number of electrons with $m_s=-\frac{1}{2}$ and $n=4$ is $\frac{32}{2}=16$