Question

Chemists use a wide array of techniques for determining the exact composition and structure of a compound. One of the most robust and interesting of these is nuclear magnetic resonance (NMR) spectroscopy. In this problem, you will see how NMR spectroscopy allows for the precise determination of the structure of an organic compound. Nuclei with odd numbers of neutrons or protons have a magnetic moment. In the presence of a strong magnetic field, some nuclei will align parallel and some will align antiparallel to the field. If a sample is subjected to electromagnetic radiation with photon energy equal to the difference in energy between the two nuclear alignment states, some nuclei in parallel states will absorb a photon and flip to antiparallel states.

Suppose that a small shift Δf in the frequency of the absorbed radiation is observed. This shift is attributed to a small change Δμ in the magnetic moment. What is the value of Δμ ?
Express your answer in terms of Δf , B , and h .

Answer 1

Δμ = hΔf/B

Step-by-step explanation:

If the photon energy , ΔE = hΔf where Δf = small frequency shift and since the potential energy change of the magnetic dipole moment μ in magnetic field B from parallel to anti-parallel state is ΔU = ΔμB. where Δμ = small shift in magnetic moment.

Since the magnetic energy change equals the photon energy,

ΔE = ΔU

hΔf = ΔμB

Δμ = hΔf/B