Question
Raman rotational spectra of was observed with Hg light with Rayleigh line at
. Stokes lines were observed at
. Draw the rotational energy level diagram with Stokes and anti Stokes lines.
Answer :
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We are asked to analyze the Raman rotational spectrum of ( \text{H}_2 ) and draw the rotational energy levels with the observed Stokes and anti-Stokes lines. Let's solve this step by step manually. --- Given: * Rayleigh line: ( \tilde{\nu}_0 = 2294 \ \text{cm}^{-1} ) * Stokes lines: ( \tilde{\nu}_S = 22581, 22337, 22094, 21851 \ \text{cm}^{-1} ) Step 1: Calculate Raman shifts Raman shift ( \Delta \tilde{\nu} = \tilde{\nu}_0 - \tilde{\nu}_S ) 1. ( \Delta \tilde{\nu}_1 = 22940 - 22581 = 359 \ \text{cm}^{-1} ) 2. ( \Delta \tilde{\nu}_2 = 22940 - 22337 = 603 \ \text{cm}^{-1} ) 3. ( \Delta \tilde{\nu}_3 = 22940 - 22094 = 846 \ \text{cm}^{-1} ) 4. ( \Delta \tilde{\nu}_4 = 22940 - 21851 = 1089 \ \text{cm}^{-1} ) --- Step 2: Relation with rotational constant ( B ) For a Raman-active diatomic molecule: * Allowed rotational transitions: ( \Delta J = 0, \pm 2 ) * Stokes lines: ( \tilde{\nu} = \tilde{\nu}_0 - 6B, \tilde{\nu}_0
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