detailed solution

Correct option is C

Sets of quantum numbers $n,$ $l, m_l, m_s$  correspond to a valence electron in a neutral atom of arsenic (As) is $4,0,0,-\frac{1}{2}$

We choose a $4s$ electron just out of convenience. Then for that electron…

• It must fall within the energy range indicated by $n=4$.
• The angular momentum of $S$ orbitals, which are spherically shaped, is zero, hence $l=0$
• One $4s$ orbital is the only one that can exist. $m_l$ range is constrained to the set {$0$} when $l=0$. There is only one orbital because each value of $m_l$ is equivalent to one.
• Depending on the value of $m_s$, each electron can have a spin-up or spin-down of 1/2. There are multiple options because this orbital is already full.

So, there are two possibilities for a 4s electron.

$\left(n,l,m_l,m_s\right)=\left(4,0,0,+\frac{1}{2}\right)$

$\left(n,l,m_l,m_s\right)=\left(4,0,0,-\frac{1}{2}\right)$

Hence, option C is correct.