Discussion
An irradiated sample of MgO has a strong ESR line at 0.163 T when the ESR spectrometer is operating at 9.4 GHz. The g value of the ESR line of MgO will be :
Answer: C
The g value is 4.13.
Rearrange the resonance condition \(h\nu = g\mu_{B}B\):
\[ \begin{aligned} g &= \frac{h\nu}{\mu_{B}B} \\ &= \frac{6.626 \times 10^{-34} \times 9.4 \times 10^{9}}{9.274 \times 10^{-24} \times 0.163} \\ &= \frac{6.228 \times 10^{-24}}{1.512 \times 10^{-24}} \approx 4.12 \end{aligned} \]
which matches 4.13 within rounding. A free-electron line (g about 2.0) at 9.4 GHz would sit near 0.336 T; the line here occurs at about half that field, so g is about twice as large.
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