Question

How many electrons in an atom may have the following quantum numbers?
(a) n = 4, $m_{s}$ = - 1/2
(b) n = 3, l = 0

Answer 1

Given from the question:

a)         The principle quantum number is n=4  

The spin quantum number is $m_{s}$ = $-\frac{1}{2}$  

For n = 4,

There are 4 orbitals possible, they are s, p, d and f

s = 1; p=3; d=5; f= 7

Therefore, number of electrons can be = 1+3+5+7 =16  electrons

b)       Similarly, for principle quantum number n = 3 and

Angular quantum number $l=0$

The orbital is 3s = 2 electrons