chapter 7/8/9

Question 1

What property must a diatomic molecule possess for it to undergo pure rotational transitions? What consequences does this have for the pure rotational spectra of N2, RbCs and HD?

Answer 1

Question 2

In the pure rotational spectrum of NaCl why are the spectral lines equally spaced? How does this spacing depend on the reduced mass of the nuclei in the molecule?

Answer 2

Question 3

What are meant by the expressions P-branch and R-branch when referring to vibrationrotation spectra of diatomic molecules?

Answer 3

Question 4

Answer 4

Question 5

How does the Franck-Condon principle affect transitions between two different electronic states in a diatomic molecule?

Answer 5

Question 6

Give expressions for the magnetic dipole moments associated with the total electron spin and the total electron orbital angular momentum in an atom.

Answer 6

Question 7

Answer 7

Question 8

In levels with spin-orbit splittings, what criterion is used to distinguish between the situations in which an external magnetic field is considered strong and weak? What are the good quantum numbers of the atom in a weak field? What are the good quantum numbers of the atom in a strong field?

Answer 8

In levels with spin-orbit splittings an external magnetic field is considered weak if the Zeeman energy shift of the sublevel with the largest magnetic dipole moment is much less than the spin-orbit energy splitting. Good quantum numbers in a weak magnetic field are n, L, S, J and MJ . Good quantum numbers in a strong magnetic field are n, L, S, ML and MS.

Question 9

What is the Land´e g-factor?

Answer 9

Question 10

In addition to the magnetic dipole moments associated with the electron spin and orbital angular momentum, what other sources of magnet dipole moments exist within atoms? What quantum numbers do the interactions of these other magnetic dipole moments with the electron spin, and orbital angular momentum, magnetic dipole moments lift the energy degeneracy of?

Answer 10

Magnetic dipole moments are also be associated with non-zero nuclear spins, ~I, in atoms. The interactions of these nuclear magnetic moments with the electron spin, and orbital angular momentum magnetic moments lift the energy degeneracy of the hyperfine states with different values of F, the total angular momentum quantum number including nuclear spin (F~ = J~ + ~I )

Question 11

Answer 11

Question 12

What conditions are required for an atomic energy level to undergo a quadratic Stark energy shift in the presence of an externally applied electric field? What conditions are required for an atomic energy level to undergo a linear Stark energy shift in the presence of an externally applied electric field?

Answer 12

Question 13

Answer 13

Question 14

Give expressions, in terms of field-free atomic orbitals, for the wavefunctions of the n = 2 energy levels in the H atom in an externally applied electric field.

Answer 14

Question 15

What happens to atomic electrons in very strong electric fields? How are these very strong fields characterised?

Answer 15

Question 16

In particle scattering experiments: What is meant by the total collision cross section? What is meant by the differential cross section?

Answer 16

The total collision cross-section is the effective area, normal to the direction of incidence, provided by the target to an incoming projectile. The differential cross-section is the particle flux scattered by each target particle into a solid angle dΩ, divided by the incoming particle intensity.

Question 17

At a fixed collision energy, in general how do the total collision cross-sections for collisions between two polar molecular ions, differ from those between two neutral polar molecules?At a fixed collision energy, in general how do the total collision cross-sections for collisions between two polar molecular ions, differ from those between two neutral polar molecules?

Answer 17

Two ions interact via the Coulomb interaction which depends on 1/r. This is a strong long-range interaction which leads to comparatively large total collision crosssections. Two neutral polar molecule interact via the electric dipole-dipole interaction. This depends on 1/r3 . At an equal inter-particle separation, the dipole-dipole interaction is weaker than the Coulomb interaction and therefore not as long-range. Consequently, the total collision cross sections are generally smaller those for collisions between the two molecular ions