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For a diatomic molecule, the rotational Raman lines are spaced by ( 2B ), where ( B ) is the rotational constant in wavenumbers (( \text{cm}^{-1} )). The first Stokes line corresponds to a transition ( J = 0 \to J = 2 ), giving a shift of ( \Delta \tilde{\nu} = 6B ). Given: [ \Delta \tilde{\nu} = 346 \ \text{cm}^{-1} = 6B ] [ B = \frac{346}{6} = 57.6667 \ \text{cm}^{-1} \approx 57.67 \ \text{cm}^{-1} ] The rotational constant ( B ) is related to the bond length ( r ) by: [ B = \frac{h}{8 \pi^2 c I} \quad \text{with} \quad I = \mu r^2 ] where ( \mu ) is the reduced mass of the molecule. Rewriting: [ r = \sqrt{\frac{h}{8 \pi^2 c \mu ____ ______ _______ ____ ______ ________ _______ _____ ______.
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