What are the total angular momentum states for l = 3, s = ½?

[acusanelli]

Homework Statement

a) Identify the different total angular momentum states possible for the case l = 3, s = ½.

b) What is the minimum angle the angular momentum vector may make with the z-axis in the case of i) l = 3 and ii) l = 1?


c) A hydrogen atom in its ground state is subjected to an external magnetic field of 1.0 T. Find the difference in energy between the spin-up and spin-down states.


d) A hydrogen atom is subjected to a magnetic field B strong enough to completely overwhelm the spin-orbit coupling. Into how many levels would the 2p level split? What would be the spacing between these levels?

The Attempt at a Solution

dont know how to set up this problem but i know the answer to c is ΔU = 1.16 X 10-4 eV. Please help me set up this problem so that I can solve it

 

[nickjer]

Well for (a) there is a method for adding angular momentum. I suggest you skim your book and notes for this. We can't really just give you the answer. Look for keywords like "addition of angular momentum".