Discussion
A carbon-hydrogen stretch appears at \( 2900 \ \mathrm{cm^{-1}} \). Replacing the hydrogen with deuterium moves it to about
Answer: B
Doubling the light atom's mass changes the reduced mass and hence the frequency:
\[ \begin{aligned} \frac{\nu_{D}}{\nu_{H}} &= \sqrt{\frac{\mu_{H}}{\mu_{D}}} \\ &\approx \frac{1}{1.36} \end{aligned} \]
giving about 2130 reciprocal centimetres. Halving would be right only if the frequency went as one over the mass rather than its square root. Deuterium substitution is used deliberately to confirm which bands involve hydrogen, since the shift is large and predictable.
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