Discussion
The rotational spectrum of a molecule is sensitive to isotopic substitution of atoms in the molecule. If the ratio of the rotational constant B′ of 13C16O to the constant B of 12C16O is 0·956; and if the first rotational line for 12C16O is observed at 3·84 cm−1, that for 13C16O will be observed at :
Answer: D
The line for \( ^{13}\text{C}^{16}\text{O} \) is at 3·67 cm−1.
The first rotational line, \( J = 0 \to 1 \), lies at \( 2B \), so it scales directly with the rotational constant:
\[ \bar{\nu}' = 3.84 \times 0.956 = 3.67\ \text{cm}^{-1} \]
The heavier \( ^{13}\text{C} \) raises the moment of inertia and lowers B, so the line must move to a lower wavenumber. 4·79 and 3·87 cm−1 move it up, and 2·89 cm−1 is far too large a shift for a ratio of 0·956.
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