Question

How many electrons in an atom may have the following quantum numbers?
$n=4,m_s=-1/2$

Answer 1

n = 4 , so there are 32 electrons present in 4rth orbit $(2n^2=2\times 2^2=32)$

If 32 electrons then there must be a 16 orbitals and each orbital contain 2 electrons one have $m_s$value -1/2 and other have $m_s$value +1/2

So there are 16 electrons have quantum number n = 4 and $m_s$ value -1/2