CHEM 442 Lecture 37 Problems
37-1. Calculate the values of Bohr magneton and nuclear magneton using electron
charge, electron mass, proton mass, and Planck’s constant.
37-2. Calculate the magnetic field (in units of T) in the 500 MHz proton NMR. Use the
result of 37-1 and nuclear g-factor of 5.586 for proton.
37-3. Using the first-order time-independent perturbation theory, show that, under a static
magnetic field B, the energy level of a d-orbital in a hydrogenic atom is split into 5
evenly spaced levels with an energy difference of mB B .
37-4. Explain why -spin electron’s energy increases by a magnetic field, whereas -spin
proton’s energy increases.
37-5. Explain why the intensity of a NMR signal increases as the square of the applied
magnetic field. Explain why the intensity is inversely proportional to the temperature.
37-6. Define a chemical shift and show that it is independent of the applied magnetic
field.
37-7. Rationalize the fact that the proton chemical shift of -COOH is greater than that of
–CH3.
37-8. Explain in detail why the CH3 peak of the CH3CH2OH (ethanol) proton NMR
spectrum is split into 3 peaks with intensity ratio of 1:2:1.
37-9. Explain in detail why the CH2 peak of the CH3CH2OH (ethanol) proton NMR
spectrum is split into 4 peaks with intensity ratio of 1:3:3:1.
37-10. Explain why protons in OH or CH2 do not affect the CH2 peak’s hyperfine
structure in the spectrum of 37-9?
37-11. What is “Fermi contact”? How does it explain the propensity of nearby electron
and proton to have anti-parallel spins?
37-12. Rationalize the fact that 1JHH is positive and 2JHH tends to be negative.