Multi-Electron Atoms

Question 1

What is the problem with multi-electron atoms?

Answer 1

We cannot solve the TISE analytically for many electrons - we need approximations.

Question 2

What is the ludicrously independent electron approximation?

Answer 2

Each electron in a multi-electron atom has a hydrogen-like wave function independent of all the others.

Question 3

What is the equation for the energy in the ludicrously independent electron approximation?

Answer 3

En = -Z^2/n^2 *E(Ry)

Question 4

What is meant by ionisation energy?

Answer 4

Energy needed to remove most weakly bound electron from an atom.

Question 5

What happens to the electrons in the ludicrously independent electron approximation?

Answer 5

All electrons would occupy lowest n=1 state: 1s.

Question 6

What do we need to correct in the ludicrously independent electron approximation?

Answer 6

More than 1 electron cannot occupy the same quantum state (n, l, j, m(j)) in an atom.

Question 7

Which order do we fill up the available quantum states?

Answer 7

From high binding energy to low.

Question 8

How does the spin fill up when increasing electron number?

Answer 8

Fills up with up spin then fills with down spin (so if has 3 parts, will fill up with 3 ups then 3 downs).

Question 9

Where do the groups appear on the periodic table?

Answer 9

Right hand side.

Question 10

Where do the transition elements appear on the periodic table?

Answer 10

Middle.

Question 11

Describe inert gases.

Answer 11

Filled shell - stable and unreactive.

Question 12

Describe alkali metals.

Answer 12

Filled shells + 1 electron. Easy to ionise by losing outer electron.

Question 13

Describe the halogens.

Answer 13

1 electron short of a filled shell -> they like to acquire an electron e.g Cl + e(+) -> Cl(-)

Question 14

What is the central field approximation?

Answer 14

Electrons move in a potential due to the nucleus screened by all electrons in more inner shells.

Question 15

At different distance r outside an electron with 3 protons and 2 electrons orbiting, what does an electron see?

Answer 15

A large enough r, electrons sees 1+ only (3+ + 2-). At low r an electron sees 3+

Question 16

What is the screened potential?

Answer 16

No longer 1/r -> need to tweak R(r).

Question 17

What is Hund’s first rule?

Answer 17

Spins prefer to be aligned rather than anti-aligned or paired.

Question 18

Why is Hund’s rule a thing?

Answer 18

Total Ψ has to be antisymmetric: Ψ = Ψ(spin)*Ψ(space) -> symmetric Ψ(spin) must go with antisymmetric Ψ(space) and vice versa.

Question 19

What is the Pauli Exclusion Principle?

Answer 19

No two electrons in an atom can have the same set of quantum numbers.

Question 20

What is meant by exchange symmetry?

Answer 20

When |Ψ(r1,r2)|^2 = |Ψ(r2, r1)|^2 -> because electrons are indistinguishable.

Question 21

How can we use exchange symmetry to determine whether a particle is a boson or a fermion?

Answer 21

If exchange symmetry is even then they’re bosons, if odd then fermions (odd if Ψ(r1,r2) = -Ψ(r2,r1)