- #1
whatapples
Homework Statement
This is not a homework problem. It's an example in a textbook.
3 electrons.
For ##S=3/2##, we have that
$$
m_{s_1}
= m_{s_2}
= m_{s_3} = 1/2
$$
Therefore by the Pauli Exclusion principle,
$$
m_{l_1}
\neq m_{l_2}
\neq m_{l_3}
$$
and they take the values ##-1,0,1## respectively since each electron has ##l=\{0,1\}##. I understand so far. Then it says that ##^4P## and ##^4D## and ##^4F## are excluded because of this. This is where I got confused. Why is this?And why is it that ##^4S## is allowed?
Homework Equations
The Attempt at a Solution
We know that the ##s## quantum number is the same for all and that ##l## is the same for two of the electrons but those two can always have a different ##m_l##. So ##L=0## is the only ##L## allowed? Why?