Question

list all possible quantum states for n=4 and l=1

Answer 1

We know that, a quantum states are described by 4 quantum numbers: Principal Quantum Number (n), Angular momentum quantum number (l), magnetic quantum number (m_l), and spin quantum number (m_s). (n, l, m_l, m_s)

The angular moentum quantum number can varry from 0 to (n-1).

The magnetic quantum number (m_l) has a range of -l,...,0,...,l.

And spin quantum numbers can only have two values +1/2 and -1/2.

Given, n = 4 and l = 1 .

So, the values of m_l are -1,0,1.

Hence, there are six possible quantum states for n=4 ad l =1. They are (4,1,-1, -1/2), (4,1,-1,+1/2), (4,1,0,-1/2), (4,1,0,-1/2), (4,1,1,-1/2), and (4,1,1,+1/2).