Atomic spectra

Question 1

How is the spin quantum number defined?

Answer 1

s
s = 1/2

Question 2

What is the consequence of spatial and spin wavefunctions not being allowed to be the same?

Answer 2

Two electrons with a symmetric spin wavefunction (i.e. two parallel spins, triplet state) cannot occupy the same spatial wavefunction (orbital)

Question 3

What is an added complication for spin-orbit coupling?

Answer 3

the magnetic dipoles from the spin angular momentum and the orbital angular momentum also interact

Question 4

What are we concerned about in atomic spectroscopy?

Answer 4

with one state of an atom (defined by an electronic configuration) absorbing or emitting a quantum of light to generate another state via a transition

Question 5

What are orbitals?

Answer 5

They are wavefunctions for the electrons - they describe the space which electrons occupy

Question 6

Degenerate states

Answer 6

Different states with the same energy

Question 7

Term

Answer 7

Represents one or more states with the same energy

Question 8

Spin multiplicity

Answer 8

The number of potential orientations of the spin angular momentum corresponding to a given total quantum number (S), for the same spatial electronic wavefunction

Question 9

Microstate

Answer 9

The arrangement of atoms or molecules in a single instant

Question 10

Why is the hydrogen atom unusual in atomic spectra?

Answer 10

It only has one electron so the energies of the ns, np and nd orbitals are degenerate - simplifies the spectra

Question 11

Triplet state of He

Answer 11

Cannot decay back to the ground state by the emission of light - but it can occur by collisions with one another or other species

Question 12

Russell- Saunders Coupling

Answer 12

The determination of J forms and L (it is an approximation that only works for light atoms)

Question 13

What is needed for a pure rotational spectrum to be observed?

Answer 13

a permanent electric dipole in the molecule as this interacts with the electric dipole of the electromagnetic radiation

Question 14

What happens to a rotational spectrum with the changing of isotopes?

Answer 14

𝜇 increases with increasing isotope mass, bond length is unaffected so B decreases

Question 15

Raman spectroscopy

Answer 15

works on the process of inelastic photon scattering

Question 16

What are the 3 different types of scattering in Raman spec?

Answer 16

• Rayleigh scatter
• Stokes Raman scatter
• Anti-Stokes Raman scatter

Question 17

Mutual exclusion rule for spec

Answer 17

For molecules with a centre of inversion (centrosymmetric), the molecules vibrations that are active in the IR spectrum are not in the Raman, and vice versa

Question 18

What are orbitals for electrons?

Answer 18

They are wavefunctions for electrons - they describe the space which electrons occupy (e.g. 1s, 2s, etc)

Question 18

What does a term represent?

Answer 18

one or more states with the same energy (degenerate states)

Question 19

What is the common unit for electric dipole?

Answer 19

1 Debye (D) = 3.336 x 10 ^-30 Cm

Question 20

What is the quantum number J?

Answer 20

Rotational quantum number

Question 21

Degeneracy of m _J

Answer 21

The degeneracy of a state with quantum number J = 2J + 1

In the absence of a magnetic or electric field all the m _J states are degenerate.

Question 22

How does isotope substitution impact the rotational spectrum?

Answer 22

𝜇 increases with increasing isotope mass but bond length is unaffected so B decreases

Question 23

Why don’t you get a vibrational (IR) spectrum in homonuclear diatomics?

Answer 23

there is no dipole moment

Question 24

What would be in the vibrational spectrum of a heteronuclear diatomic?

Answer 24

- a line for v=0 → v=1 at Ṽ (FUNDAMENTAL) - a less intense line at slightly lower wavenumber, v=1 → v=2 (HOT-BAND) - another weak line at approx 2Ṽ, v=0 → v=2 (OVERTONE)

Question 25

Selection rules for vibrational-rotational spectroscopy

Answer 25

- Δv = ±1 (& ±2 ...) - ΔJ = ±1

Question 26

Vibrational-rotational spectroscopy: ΔJ = +1

Answer 26

R branch

Question 27

Vibrational-rotational spectroscopy: ΔJ = -1

Answer 27

P branch

Question 28

How many vibrational modes are there in a non-linear molecule?

Answer 28

3n-6

Question 29

How many vibrational modes are there in a linear molecule?

Answer 29

3n-5

Question 30

What do the wavenumbers of the R and P branches mean?

Answer 30

they tell us how much energy (in cm ^-1 ) is absorbed by the molecule when it undergoes simultaneous changes in vibrational and rotational energy levels

Question 31

How does IR spectroscopy and Raman spectroscopy differ?

Answer 31

IR spectroscopy: measures how much light a molecule absorbs Raman spectroscopy: measures how light is scattered off a molecule and how the energy of the scattered light shifts

Question 32

What are the 3 types of scattering in Raman spectroscopy?

Answer 32

- Rayleigh scatter - Stokes Raman scatter (molecule gains vibrational energy) - Anti-Stokes Raman scatter (molecule loses vibrational energy)

Question 33

What is the selection rule for Raman spectroscopy?

Answer 33

Polarisability must change with varying nuclear coordinate (dɑ/dQ) ≠ 0

Question 34

For centrosymmetric molecules, when are they Raman/ IR active

Answer 34

- gerade: Raman active - ungerade: IR active