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
A)0 or 1
B)1 or 2
C)2 or 3
D)3 or 4
E)5 or 6

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
A)0 or 1 
B)1 or 2 
C)2 or 3 
D)3 or 4 
E)5 or 6

Quizplus · Accepted Answer

For an electron in a hydrogen atom, the total angular momentum J is given by the vector sum of the electron's orbital angular momentum L and its spin angular momentum S. Therefore, we have:

J = L + S

The value of j = 5/2 means that the magnitude of the total angular momentum is J = 5/2 ħ, where ħ is the reduced Planck constant.

Now, we can determine the possible values of L from the fact that the maximum value of L for a given J is given by |J - 1/2|. Therefore, we have:

|J - 1/2| ≤ L ≤ J + 1/2

Substituting J = 5/2, we get:

|5/2 - 1/2| ≤ L ≤ 5/2 + 1/2

i.e.

2 ≤ L ≤ 3

Therefore, the possible values of the orbital angular-momentum quantum number L are 2 or 3. Hence, the correct answer is C) 2 or 3.

The Total Angular Momentum of a Hydrogen Atom in a Given