Atomic spectra Flashcards
How is the spin quantum number defined?
s
s = 1/2
What is the consequence of spatial and spin wavefunctions not being allowed to be the same?
Two electrons with a symmetric spin wavefunction (i.e. two parallel spins, triplet state) cannot occupy the same spatial wavefunction (orbital)
What is an added complication for spin-orbit coupling?
the magnetic dipoles from the spin angular momentum and the orbital angular momentum also interact
What are we concerned about in atomic spectroscopy?
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
What are orbitals?
They are wavefunctions for the electrons - they describe the space which electrons occupy
Degenerate states
Different states with the same energy
Term
Represents one or more states with the same energy
Spin multiplicity
The number of potential orientations of the spin angular momentum corresponding to a given total quantum number (S), for the same spatial electronic wavefunction
Microstate
The arrangement of atoms or molecules in a single instant
Why is the hydrogen atom unusual in atomic spectra?
It only has one electron so the energies of the ns, np and nd orbitals are degenerate - simplifies the spectra
Triplet state of He
Cannot decay back to the ground state by the emission of light - but it can occur by collisions with one another or other species
Russell- Saunders Coupling
The determination of J forms and L (it is an approximation that only works for light atoms)
What is needed for a pure rotational spectrum to be observed?
a permanent electric dipole in the molecule as this interacts with the electric dipole of the electromagnetic radiation
What happens to a rotational spectrum with the changing of isotopes?
𝜇 increases with increasing isotope mass, bond length is unaffected so B decreases
Raman spectroscopy
works on the process of inelastic photon scattering
What are the 3 different types of scattering in Raman spec?
- Rayleigh scatter
- Stokes Raman scatter
- Anti-Stokes Raman scatter
Mutual exclusion rule for spec
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
What are orbitals for electrons?
They are wavefunctions for electrons - they describe the space which electrons occupy (e.g. 1s, 2s, etc)
What does a term represent?
one or more states with the same energy (degenerate states)
What is the common unit for electric dipole?
1 Debye (D) = 3.336 x 10 -30 Cm
What is the quantum number J?
Rotational quantum number
Degeneracy of m J
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.
How does isotope substitution impact the rotational spectrum?
𝜇 increases with increasing isotope mass but bond length is unaffected so B decreases
Why don’t you get a vibrational (IR) spectrum in homonuclear diatomics?
there is no dipole moment
What would be in the vibrational spectrum of a heteronuclear diatomic?
- 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)
Selection rules for vibrational-rotational spectroscopy
- Δv = ±1 (& ±2 …)
- ΔJ = ±1
Vibrational-rotational spectroscopy: ΔJ = +1
R branch
Vibrational-rotational spectroscopy: ΔJ = -1
P branch
How many vibrational modes are there in a non-linear molecule?
3n-6
How many vibrational modes are there in a linear molecule?
3n-5
What do the wavenumbers of the R and P branches mean?
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
How does IR spectroscopy and Raman spectroscopy differ?
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
What are the 3 types of scattering in Raman spectroscopy?
- Rayleigh scatter
- Stokes Raman scatter (molecule gains vibrational energy)
- Anti-Stokes Raman scatter (molecule loses vibrational energy)
What is the selection rule for Raman spectroscopy?
Polarisability must change with varying nuclear coordinate
(dɑ/dQ) ≠ 0
For centrosymmetric molecules, when are they Raman/ IR active
- gerade: Raman active
- ungerade: IR active
