# Possible partial waves for photoelectron of nitrogen

• thecommexokid

## Homework Statement

(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?

## Homework 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.

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Partial wave analysis is a method used in quantum mechanics to describe the behavior of a particle, such as a photoelectron, as it interacts with a potential. It involves breaking down the wavefunction of the particle into different partial waves, each with its own angular momentum and parity. In this case, the outgoing photoelectron can have different partial waves, each with its own angular momentum and parity, depending on the direction in which it is ejected from the atom.

In the case of the nitrogen atom, the possible partial waves for the outgoing photoelectron would be 2P1/2odd, 2P3/2odd, 3P1/2even, and 3P3/2even. These correspond to different combinations of angular momentum and parity values for the photoelectron. For example, the 2P1/2odd partial wave has an angular momentum of 1/2 and a parity of -1, while the 3P3/2even partial wave has an angular momentum of 3/2 and a parity of +1.

By analyzing the partial waves, scientists can gain a better understanding of the interactions between particles and potential fields, such as in the case of photoabsorption in the nitrogen atom.