Determening allowed states in atoms

[jonas_nilsson]

Hello,
there is one thing about atomic states I don't understand. I try to look at what states are possible for a np^2 configuration (that is, all lower shells are filled and don't contribute to the case). For example my textbook says that the $$~^1 P$$ state is not allowed because of the Pauli principle.
But now, let's have a look at what $$^1 ~P$$ means:
L = 1
S = 0
The spins are clearly anti-parallel. For L = 1 we have M_L = -1,0,1. I don't see any problem finding m_l's adding up to those M_L's without breaking the Pauli principle. So what am I not getting?

 

[ZapperZ]

Hello,
there is one thing about atomic states I don't understand. I try to look at what states are possible for a np^2 configuration (that is, all lower shells are filled and don't contribute to the case). For example my textbook says that the $$~^1 P$$ state is not allowed because of the Pauli principle.
But now, let's have a look at what $$^1 ~P$$ means:
L = 1
S = 0
The spins are clearly anti-parallel. For L = 1 we have M_L = -1,0,1. I don't see any problem finding m_l's adding up to those M_L's without breaking the Pauli principle. So what am I not getting?

Er... unless I misunderstand your notation, for n=1, you only have L=0 as the only possible angular momentum state. L=1 doesn't exist. Only for n=2 do you have L=0 and 1.

Zz.

 

[jonas_nilsson]

No I don't mean n=1 but rather 2S+1 = 1. I tried to hang the "1" a bit higher with tex-code, but it didn't work out perfectly I guess. To clarify: with upper case I mean the total spin/orbital angular momentum of all the electrons and with lower case spin/orbital angular momentum of an individual electron.