Discussion
A proton spectrometer operates at 11.74 T. Given \( \gamma / 2\pi = 42.58 \) MHz per tesla, what is the proton frequency?
Answer: A
Multiplying the field by the gyromagnetic ratio in frequency units gives the answer directly:
\[ \nu = 42.58 \times 11.74 \approx 500 \]
so the instrument is a 500 MHz machine. The same arithmetic puts 400 MHz at 9.4 T and 600 MHz at 14.1 T, and those three fields cover most departmental spectrometers. Naming an instrument by its proton frequency rather than its field is a convenience: the frequency is what the chemist tunes and what sets the dispersion of the spectrum.
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