Discussion
The rotational constant (usually denoted as B) for the oxygen molecule is
Answer: A
The rotational constant is B = 1.2 cm-1.
The 16O nucleus has spin zero, and the ground state of O2 is 3Σg-. Nuclear spin statistics then allow only odd rotational levels (J = 1, 3, 5 ...). The first Stokes line is therefore J = 1 to J = 3, not J = 0 to J = 2. With rotational energies BJ(J + 1):
\[ \begin{aligned} \Delta\tilde{\nu} &= B(3 \cdot 4 - 1 \cdot 2) = 10B \\ 10B &= 20491 - 20479 = 12\ \text{cm}^{-1} \\ B &= 1.2\ \text{cm}^{-1} \end{aligned} \]
2.0 cm-1 is what the usual first-line shift of 6B (J = 0 to 2) would give, which is the trap here. 3.0 and 6.0 come from taking the shift as 4B or 2B.
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