Discussion
If the average separation between the adjacent lines in the rotational IR spectrum of CO molecule is 3.844 cm\(^{-1}\), then the value of rotational constant is :
Answer: B
The rotational constant is \(B = 1.922\) cm\(^{-1}\).
For a rigid rotor the rotational levels are \(F(J) = BJ(J + 1)\), and the allowed transitions \(J \rightarrow J + 1\) give lines at
\[ \bar{\nu} = 2B(J + 1) \]
so adjacent lines are separated by 2B. Hence
\[ B = \frac{3.844}{2} = 1.922\ \text{cm}^{-1} \]
Taking the spacing itself as B gives 3.844, twice the spacing gives 7.688, and 5.766 is 3B; none is the rotational constant.
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