Lecture 1

Question 1

• µ_S = -g_eµ_BS/ħ is the energy of a magnetic dipole, µ for a free electron when in a magnetic field, B. Explain all terms stated

Answer 1

• • sign as magnetic moment is antiparallel to spin
• S – quantum mechanical spin of electron (like nuclear spin in NMR)
• µ_B – Bohr magneton
• g_e – Zeeman splitting constant (2.00232)

Question 2

• what is the equation for the bohr magneton (dont need to know)

Answer 2

• µ_B = eħ/2m_e

Question 3

• What is the classical expression for magnetic dipole in a magnetic field? (dont need to know)

Answer 3

• U = -µ*B

Question 4

• What is the Hamiltonian associated with QM energy operator? (dont need to know)

Answer 4

• H = g_eµ_BBS_z/ħ
• Assumes B is along the z direction

Question 5

• Give the equation for the Energy describing the magnetic moment of a free electron

Answer 5

• E_Ms = g_eµ_BBM_s
• E doesn’t depend on quantum number s, only M_s
• Sign cancels in magnetic moment and U = -µ*B

Question 6

• Describe the splitting of the energy levels of a free electron in a magnetic field. include equations and a sketch to aid your answer

Answer 6

• Magnetic dipole transitions can be induced between the two energy levels by the magnetic field vector and an EM field (B_µw) provided the photon energy hv matches the energy level separation and has appropriate polarization

Question 7

• What is wrong with the assumption of a free electron in the absence of a magnetic field thus far and a lot throughout chemistry?

Answer 7

• An ideal system of a free electron sitting in space interacting with nothing is unrealistic, but allows easy solving of equations as gives a single line in MO
• In reality will be interacting with many things in environment causing shifts/splitting of energy levels which allow us to understand structure.

Question 8

• Give an example of a source of free electrons

Answer 8

• Free radicals

Question 9

• In UV vis light is absorbed causing movement of … in energy levels, and causing electric … to flip
• Light is associated with … and … field
• In optical absorption of … dipole transitions, … field drives this transition.
• In NMR/ESR (nuclear magnetic/electron spin) it is … dipole transitions that are driven.

Answer 9

• In UV vis light is absorbed causing movement of electrons in energy levels, and causing electric dipole to flip
• Light is associated with magnetic and electric field
• In optical absorption of electric dipole transitions, electric field drives this transition.
• In NMR/ESR (nuclear magnetic/electron spin) it is magnetic dipole transitions that are driven.

Question 10

• What is required to observe stimulated transitions between state +/- 1/2?

Answer 10

• Must be a population difference between levels
• Governed by Maxwell-Boltzmann distribution
• Always less electrons in higher level

Question 11

• If the lower energy state has more electrons why is equilibrium not an even split?

Answer 11

• Transitions from lower level to equalise populations countered by spin-lattice relaxation from higher energy state to maintain Maxwell-Boltzmann distribution
• At cooler temperatures, more in lower state