Topic 2

Question 1

What is the letter for the principal quantum number?

Answer 1

n

Question 2

What is the letter for the orbital angular momentum quantum number?

Answer 2

l

Question 3

What is the letter for the magnetic quantum number?

Answer 3

m_l

Question 4

What is the letter for the spin quantum number?

Answer 4

s

Question 5

What is the letter for the magnetic spin quantum number?

Answer 5

m_s

Question 6

In the absence of spin-orbital coupling the energy of an atomic orbital in a one-electron atom or ion, X, only depends on what?

Answer 6

On the principal quantum number, n.

Where Z is the nuclear charge, R_X is the Rydberg constant for that atom.

Question 7

What happens when n goes closer to infinity?

Answer 7

Energy and n has an inverse relationship. So the higher the n the closer to 0 energy we get as relationship is E=1/n²

Question 8

Why the energy velue of energy levels is negative?

Answer 8

As n increases, electron moves further away from the nucleus until we get n value where electron is ionised from the atom. This energy is equal 0. And as electron moves down in n, it gets more stable so we move down in energy.

Question 9

What is Rydberg constant?

Answer 9

This expression comes from solving the Schrodinger equation and getting the correct units. Note that c is in cm s^-1. The value depends on the mass of the nucleus, and so there is a drifferent Rydberg constant for each atom.ion.

Question 10

How to calculate energy difference between to energy levels?

Answer 10

Question 11

What are selection rules for spectroscopy?

Answer 11

Δn (principal quantum number) unrestricted

(orbital angular momentum quantum number) Δl=±1 (Laporte selectrion rule)

Question 12

Explain Laporte selection rule.

Answer 12

Δl=±1, meaning transitions can accur between s,p,d,f orbitals byt not within them

Question 13

How to calculate Ionisation energy?

Answer 13

IE is the energy where n is equal to infinity which is 0, minus the energy of 1s orbital which is minus. Thus ionisation energy is equal to energy of 1s orbital.

Question 14

What is atomic emission spectrometer?

Answer 14

It records emissions produced by different substances when it is burning and compares it with a known values.

Question 15

How do we analyse spectra with more then one electron?

Answer 15

We look at orbital angular momentum of each of the electrons and see how those behave inside a particular atom.

Question 16

What is the value of l for s orbital?

Answer 16

l=0

Question 17

What is the value of l for p orbital?

Answer 17

l=1

Question 18

Why adding up the angular momenta will lead to different energies?

Answer 18

Because the angular momenta of the different electrons in the atom can couple together in different ways.

Question 19

When considering spectra with more than one electron which quantum numbers we consider first and which last?

Answer 19

We will consider spin first, then orbital angular momenta, then finally the coupling between spin and orbital angular momenta.

Question 20

What is Russell-Saunders coupling?

Answer 20

Is where we allow the spins to couple together and the orbital angular momenta to couple together separately. And then only at the end to be coupled together.

Question 21

What is Clebsch-Gordan series for spin quantum number?

Answer 21

If S in the overall spin of the two-electron system, then the allowed values come from: S=s₁+s₂​, s₁+s₂​-1… |s₁-s₂​|.

So the allowed values of S are 1/2+1/2=1 and 1/2 - 1/2=0

Question 22

What are alowed values for l coupling considering Clebsch- Gordan series?

Answer 22

Values of l are integer, 0,1,2… If L is the total orbial angular momentum of the combined system, then allowed values are L=(l₁+l₂), (l₁+l₂​-1),…|l₁-l₂​|

So if l₁=2 and l₂=3, for example, then we have a highest value of 2+3=5, and the lowest value |2-3|=1.

Hence L=5, 4, 3, 2, 1

Question 23

What are the values of spin-orbital angular momentum, J?

Answer 23

We use Clebsch-Gordan series J=L+S, L+S-1,… |L-S|

So if both L and S are 1, then allowed values of J are 2, 1, 0.

Question 24

What are values of M_L of atom with more than one electron?

Answer 24

M_L=L, L-1…, -L

Question 25

What are values of M_S of atom with more than one electron?

Answer 25

M_S= S, S-1…, -S

Question 26

What atomic term symbols mean?

Answer 26

Question 27

What is the term sybol for all closed-shell atoms and ions?

Answer 27

¹S₀

Question 28

What is the term symbol for alkali metals?

Answer 28

²S_1/2

Question 29

What determines the intensity of transitions?

Answer 29

Since the final level is the same, the intensity of the transition is mostly determined by the degeneracy (2J+1) of the upper levels. Hence, we expect ratio 2:1 of intensities.

Question 30

What is boson?

Answer 30

Something which has a spin of 0, 1 or 2

Question 31

What is Pauli principle?

Answer 31

Any acceptable wavefunction must be antisymmetric with respect to the exchange of two identical fermions (e.g. electrons) and totally symmetric with respect to the exchange of identical bosons.

Question 32

Waht is Pauli exclusion principle?

Answer 32

No two electrons in an atom/ ion can have all quantum numbers the same

Question 33

What are Hund’s rules?

Answer 33

1. The term with largest S is lowest in energy
2. For a given S the term with largest L is lowest in energy
3. For a term with several levels:

• If the sub-shell is less than half full the lowest J level is lowest in energy,
• If the sub-shell is more than half full the highest J level is lowest in energy