Question

(a) Given the allowed values of the quantum numbers n,l, m and m_s of an electron in a hydrogen atom 

(b) What are the allowed numerical values of l and m for the n = 3 level? 

(c) Hence show that this level can accept 18 electrons.

Answer 1

The principle quantum number n denotes the number of stationary states in 

Bohr’s atom model. n = 1, 2, 3 ... 

l is called azimuthal or orbital angular quantum number. For a given value of n,l takes the values 0, 1, 2 ... n − 1 

The quantum number ml , called the magnetic quantum number, takes the values −l, −l + 1, −l + 2,..., +l for a given pair of n and / values. This gives the following scheme:

m_s, the projection of electron spin along a specified axis can take on two values ±1/2.

Hence the total degeneracy is 2n². For n = 3, 2 × 3² = 18 electrons can be accommodated.