Question

The spacing between two consecutive S-branch lines of the rotational Raman spectra of hydrogen gas is 243.2 cm\(^{-1}\). After excitation with a laser of wavelength 514.5 nm, the Stoke's line appeared at 17611.4 cm\(^{-1}\) for a particular energy level. The wavenumber (rounded off to the nearest integer), in cm\(^{-1}\), at which Stoke's line will appear for the next higher energy level is \(\underline{\hspace{2cm}}\).

Hint:

For rotational Raman spectra, the spacing between lines is constant, and the Stoke's line wavenumber increases by the same amount for successive energy levels.

Answer 1

Correct Answer: 17367

The Stoke's line wavenumber change is related to the rotational energy levels. The spacing between consecutive S-branch lines is given as 243.2 cm\(^{-1}\). For the next energy level, the wavenumber of the Stoke's line will increase by the same amount. So, the wavenumber for the next higher energy level is: \[ 17611.4 \, \text{cm}^{-1} + 243.2 \, \text{cm}^{-1} = 17854.6 \, \text{cm}^{-1} \] Thus, the wavenumber for the next higher energy level is \( \boxed{17855} \, \text{cm}^{-1} \).