# Possible partial waves for photoelectron of nitrogen

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1. Jan 6, 2015

### thecommexokid

1. The problem statement, all variables and given/known data

(a) The nitrogen atom has seven electrons. Write down the electronic configuration in the ground state, and the values of parity (Π), spin (S), orbital angular momentum (L), and total angular momentum (J) of the atom.

(b) If an extra electron is attached to form the N negative ion, what are its electron configuration and values of (Π, S, L, J)?

(c) If now, upon photoabsorption, the extra electron is detached to leave the nitrogen atom behind in its ground state, what are the possible partial waves for the outgoing photoelectron?

2. Relevant equations

The Aufbau principle, the Pauli exclusion principle, Hund's rules, conservation laws

3. The attempt at a solution

I believe I can do (a) and (b), though please by all means check that they are correct.

(a) Picture: $$\underset{1s0}{\boxed{\uparrow\downarrow}}\quad\underset{2s0}{\boxed{\uparrow\downarrow}}\quad\underset{2p1}{\boxed{\uparrow\phantom\downarrow}}\ \underset{2p0}{\boxed{\uparrow\phantom\downarrow}}\ \underset{2p{-1}}{\boxed{\uparrow\phantom\downarrow}}$$
Electron configuration: 1s2 2s2 2p3
S = 3/2
L = 0
J = |LS| = 3/2
Π = –1
Spectroscopist's notation, for practice: 4S3/2odd.

(b) Picture: $$\underset{1s0}{\boxed{\uparrow\downarrow}}\quad\underset{2s0}{\boxed{\uparrow\downarrow}}\quad\underset{2p1}{\boxed{\uparrow\downarrow}}\ \underset{2p0}{\boxed{\uparrow\phantom\downarrow}}\ \underset{2p{-1}}{\boxed{\uparrow\phantom\downarrow}}$$
Electron configuration: 1s2 2s2 2p4
S = 1
L = 1
J = L + S = 2
Π = 1
Spectroscopist's notation: 3P2even.

(c) Okay, so due to conservation of everything, the photoelectron must have
s = 1/2
= 1
j = 1/2
π = –1
Spectroscopist's notation: 2P1/2odd.
I'm sure this is the relevant information to answer the question; I just don't know anything about the topic of partial-wave analysis so I don't know what the question actually means.

Last edited: Jan 6, 2015
2. Jan 11, 2015