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## 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

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: 1

*s*

^{2}2

*s*

^{2}2

*p*

^{3}

*S*= 3/2

*L*= 0

*J*= |

*L*–

*S*| = 3/2

*Π*= –1

Spectroscopist's notation, for practice:

^{4}

*S*

_{3/2}

^{odd}.

(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: 1

*s*

^{2}2

*s*

^{2}2

*p*

^{4}

*S*= 1

*L*= 1

*J*=

*L*+

*S*= 2

*Π*= 1

Spectroscopist's notation:

^{3}

*P*

_{2}

^{even}.

(c) Okay, so due to conservation of everything, the photoelectron must have

*s*= 1/2

*ℓ*= 1

*j*= 1/2

*π*= –1

Spectroscopist's notation:

^{2}

*P*

_{1/2}

^{odd}.

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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