Question

The total number of hyperfine lines expected in the EPR spectrum of •CH₂OH (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

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 •CH₂OH radical:

• There are two equivalent H atoms on the CH₂ 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 CH₂ hydrogens contribute:

\[ 2 \cdot \left(\frac{1}{2}\right) + 1 = 2 + 1 = 3 \text{ lines} \]

The OH hydrogen couples independently (non-equivalent), so each of the 3 lines splits further into:

\[ 2 \cdot \left(\frac{1}{2}\right) + 1 = 2 \text{ lines} \]

Therefore, total hyperfine lines:

\[ 3 \times 2 = \boxed{6} \]