The total angular momentum of a hydrogen atom in a given excited state has the quantum number j = 5/2. The orbital angular-momentum quantum number must have the values

Question

The total angular momentum of a hydrogen atom in a given excited state has the quantum number j = 5/2. The orbital angular-momentum quantum number  must have the values

Quizplus · Accepted Answer

The total angular momentum quantum number j is the sum of the orbital angular momentum quantum number l and the electron spin quantum number s, i.e. j = l + s. For a hydrogen atom, the electron spin s = 1/2. Therefore, the possible values of l can be deduced as follows: j = 5/2 = l + 1/2, or l = 2 or 3. Since l must be less than or equal to j-1, the possible values of l are 2 or 3.

The Total Angular Momentum of a Hydrogen Atom in a Given