GATE 2021 PH – Question 32
The spacing between consecutive S-branch lines in the rotational Raman spectrum of hydrogen is $243.2\ \mathrm{cm}^{-1}$. With laser wavelength 514.5 nm, a Stokes line for one energy level appears at $17611.4\ \mathrm{cm}^{-1}$. Find the wavenumber in $\mathrm{cm}^{-1}$ for the Stokes line from the next higher energy level, rounded to the nearest integer.
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Correct answer: 17367 to 17371
Explanation
S-branch rotational Raman transitions have $\Delta J=+2$. Their Raman shifts increase by the stated constant spacing as the initial rotational level increases. A larger Stokes shift means a smaller scattered-light wavenumber. Therefore the next line is $17611.4-243.2=17368.2\ \mathrm{cm}^{-1}$, which rounds to 17368. The laser wavelength fixes the absolute excitation wavenumber but cancels in this difference.
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