Question

The quantum state of a particle can be specified by giving a complete set of quantum numbers (n,l, ml,ms). How many different quantum states are possible if the principal quantum number is n=3?

Answer 1

Explanation:

We need to find the quantum state of a particle can be specified by giving a complete set of quantum numbers (n,l, ml,ms).

We have the principal quantum number, n = 3

The value of l = n-1

l = 0,1,2,3

The value of $m_l$

$m_l=-l\ \text{to}\ +l\\\\m_l=-3,-2,-1,0,1,2,3$

The value of $m_s$

$m_s=\dfrac{-1}{2},\dfrac{+1}{2}$

Hence, this is the required solution.