- #1
Kara386
- 208
- 2
Homework Statement
Two electrons in helium have ##l_1=1## and ##l_2=3##. What are the values of ##L## and ##S##? From this, deduce the possible values of ##J## and find how many quantum states this excited state of helium can occupy.
Homework Equations
The Attempt at a Solution
For ##L## the allowed values are given by ##L= \hbar m##, so for ##l_1=1## ##L = hbar##, ##0## and ##L=-\hbar##.
For ##l_2##,
##L = -3\hbar##, ##-2\hbar##, ##-\hbar##, ##0##, ##\hbar##, ##2\hbar## and ##L=3\hbar##.
For ##S## the allowed values are again the eigenvalues which are ##\hbar m_s##, ##m_s## runs from ##-s## to ##s## in integer steps. Electrons have ##s=\frac{1}{2}##, so
##S = -\frac{1}{2}\hbar## or ##S = \frac{1}{2} \hbar##.
I'm not sure how to work out ##J##, in my lecture notes it says for a single electron ##j = l \pm \frac{1}{2}## but doesn't say how that changes for multiple electrons. ##J=\hbar m_j## where ##m_j## runs from ##-j## to ##j##.
For the last part, I think for every combination of ##L##, ##J## and ##S## there are ##2J+1## quantum states. So I think the main question I have is: how can I work out the allowed values of ##J##? Can I work them out individually for each electron using ##j = l \pm \frac{1}{2}## and then add them?