What is the energy of the photon that will be absorbed by a 1H nucleus in a 1.5 Tesla magnetic field? How does this compare in energy to a 2x1019 Hz x-ray photon? What is the ionization potential for a typical organic molecule? Which of the two photons will ionize the molecule?

g = 42.58 MHz/T

The energy absorbed by a 1H nucleus is:
EH = h ν
EH = h γ Bo
EH = 6.626x10-34 Js * 42.58x106 Hz/T * 1.5 T
EH = 4.23x10-26 J

The energy of a ν=2x1019 Hz X-ray photon is:
EX = hν EX = 6.626 x 10-34 Js * 2x1019 Hz = 1.33x10-14 J

How the two energies compare?
EX / EH  = 1.33 x 10-14 J / 4.23 x 10-26 J = 3.14 x 1011
The energy of the X-ray photon is 1011 times more than the 1H photon energy.

Based on the figure in the text, the ionization potential for an organic compound is approximately 6x10-19 J. Therefore only the x-ray photon can ionize the molecule.