Finding components of 2s2p configuration using LS coupling

[omicgavp]

Homework Statement

The lowest excited states of the Be atom correspond to a 2s2p configuration of optically active electrons. What ^2s+1L_j components originate in this configuration? Assume that Hund's rules hold for the multiplet and deduce the ordering of the energy levels. Refer to a table of beryllium levels to see if the ordering occurs as predicted.

Homework Equations

l=|l₁-l₂|,|l₁-l₂|+1,...,l₁+l₂-1,l₁+l₂


j=|l-s|,|l-s|+1,...,l+s-1,l+s

The Attempt at a Solution

spin-orbital assignments of 2s2p configuration:
(l₁=0,s₁=1/2) and (l₂=1,s₂=1/2)

So that,
total spin states: s=0 and 1
and
l=0,1, and 2
......?
I don't know what to do next.

Answer at the back of the book:
³P_0,1,2,¹P₁

 

[ygolo]

You pretty much have it. Except, I don't believe you calculated the possible l values properly.

|1-0|=1, so only l=1 works.

Now, all you have to do is use Hund's rules to find the order.

This will lead to the answer in the book.