Question

The total number of hyperfine lines expected in the EPR spectrum of \(\cdot\)CHsubscript{2OH (radical) is ___________ (in integer).}

Hint:

When multiple non-equivalent sets of nuclei are present, calculate the number of EPR lines by multiplying the number of splittings from each nucleus: \[ {Total lines} = (2n_1I_1 + 1)(2n_2I_2 + 1)\ldots \] Always consider nuclear spin and equivalence of nuclei.

Answer 1

Correct Answer: 6

The EPR (Electron Paramagnetic Resonance) spectrum shows hyperfine splitting due to interactions of the unpaired electron with nearby nuclei that have a non-zero nuclear spin. In the \(\cdot\)CHsubscript{2}OH radical: There are two equivalent H atoms on the CHsubscript{2} group. There is one H atom on the OH group.
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: \[ 3 \times 2 = \boxed{6} \]