Angle calculation from Atomic Term Symbol

[pdubbbs]

Homework Statement

Calculate the smallest angle (in degrees) that the total angular momentum of an atom in a ⁷D term can make with the z-axis.

Homework Equations

^2S+1L_J

The Attempt at a Solution

Given that the total angular momentum of the atom is defined by the quantum number J, I started by finding all possible resultant J values for the term:

⁷D:

2(S)+1 = 7
S = 3

D = L = 2

J = { (L+S),(L+S-1), ... , (L-S) }
Thus, J = 5, 4, 3, 2, 1

This is where I'm stuck, I literally have no clue how to go further in the angle calculation. This is a review problem for an exam, and it was never covered in class. Hopefully someone can share some insight. Thanks for any help!

 

[ideasrule]

Your work is correct so far. When you measure the total angular momentum, what are the possible values? When you measure the projection of the angular momentum along the z axis, what are the possible values? You want the ratio of jz to ||j|| to be as high as possible, in order to minimize the angle that the total angular momentum makes with the z axis.