The total number of hyperfine lines expected in the EPR spectrum of \(\cdot\)CHsubscript{2OH (radical) is ___________ (in integer).}
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Correct Answer: 6
Solution and Explanation
All H nuclei have spin \( I = \frac{1}{2} \). For \(n\) equivalent nuclei with spin \( I \), the number of hyperfine lines is given by \( 2nI + 1 \). The two CHsubscript{2} hydrogens contribute: \[ 2 \cdot \left(\frac{1}{2}\right) + 1 = 2 + 1 = 3 { lines} \] The OH hydrogen couples independently (non-equivalent), so each of the 3 lines splits further into: \[ 2 \cdot \left(\frac{1}{2}\right) + 1 = 2 { lines} \] Therefore, total hyperfine lines: \[ 3 \times 2 = \boxed{6} \]
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