GATE 2026 PH – Question 34
Raman spectrum of a molecule was recorded using a source of wavelength 5000 Å. The first Stokes line is observed at 5100 Å. The first anti-Stokes line will appear at a wavelength L (in Å). The value of L (rounded off to nearest integer) is _____
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Correct answer: 4904
Explanation
In Raman scattering the scattered light is shifted from the source frequency by the molecular vibrational frequency $\Delta\tilde\nu$:
- **Stokes line:** $\tilde\nu_S=\tilde\nu_0-\Delta\tilde\nu$ (lower frequency, longer wavelength),
- **anti-Stokes line:** $\tilde\nu_{AS}=\tilde\nu_0+\Delta\tilde\nu$.
**Wavenumbers (in terms of $1/\lambda$):** the source is at 5000 Å and the Stokes line at 5100 Å:
$$\Delta\tilde\nu=\frac1{5000}-\frac1{5100}\ \text{Å}^{-1}.$$
**Anti-Stokes line:**
$$\frac1{\lambda_{AS}}=\frac1{5000}+\Delta\tilde\nu=\frac2{5000}-\frac1{5100}=4\times10^{-4}-1.9608\times10^{-4}=2.0392\times10^{-4}\ \text{Å}^{-1}.$$
$$\lambda_{AS}=\frac1{2.0392\times10^{-4}}=\mathbf{4904\ \text{\AA}}.$$