Many Electrons in an Atom

Question 1

What is ms quantum number

Answer 1

It is the quantum number related to the spin of the electron
ms= ±1/2

Question 2

Can we solve non hydrogenic wavefunctions

Answer 2

They are practically unsolvable however we can make approximations with some principles

Question 3

Pauli exclusion principle

Answer 3

No two electrons can have the same set of quantum numbers, so maximum number of electrons in an orbital is 2

Question 4

Hund’s rule

Answer 4

Electrons will fill up degenerate orbitals singly with the same spin before doubling up

Question 5

Aufbau principle

Answer 5

Electrons fill up orbitals in order of increasing energy.
It doesn’t go up per orbital due to shielding

Question 6

Shielding

Answer 6

Electron repulsion between orbitals, greater the penetration of the electron the less shielding it will experience

Question 7

Penetration

Answer 7

How close the electron can get to the nucleus

Question 8

Z effective

Answer 8

Effective nuclear charge on an electron Z_ef f= Z-σ where Z is the nuclear charge from the nucleus and σ is the electron charge multiplied by the kernel electrons

Question 9

Kernel electrons

Answer 9

The number of electrons that are not in the valence shell

Question 10

Hydrogen energy level equation

Answer 10

E_n = -hcR/n^2

n is the principle quantum number and R is the Ryberg constant

Question 11

Delta E for E_n level for hydrogen

Answer 11

Use previous equation but have Delta E = E initial - E final
Rearrange with equation for Energy of a photon with wavelength and solve which is =kT/Bhc after we sub for ΔE.

Question 12

How to work out maximum occupied energy level:

Answer 12

Differential with respect to J = 0 and solve to get Jmax = 1/2 ((2kt)/(Bhc))^1/2 -1/2