Discussion
For proton (1H), placed in a magnetic field of 2.3 Tesla, the resonant frequency observed in an NMR spectrometer is (Given : \(g_{N} = 5.58\), \(\beta_{N} = 5.05 \times 10^{-27}\) JT-1 and h = 6.6 × 10-34 Js)
Answer: D
The resonant frequency is about 100 MHz.
NMR resonance occurs when \(h\nu = g_{N}\beta_{N}B\):
\[ \begin{aligned} \nu &= \frac{g_{N}\beta_{N}B}{h} \\ &= \frac{5.58 \times 5.05 \times 10^{-27} \times 2.3}{6.6 \times 10^{-34}} \\ &= 9.8 \times 10^{7}\ \text{Hz} \approx 100\ \text{MHz} \end{aligned} \]
That matches the rule that protons resonate at about 42.6 MHz per tesla, so a 2.35 T magnet makes a '100 MHz' spectrometer. 1000 MHz would need about 23 T, and the kHz and 1 MHz options are far too low.
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