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GATE 2021 CY – Question 60

Physical Chemistry · Spectroscopy: Atomic spectroscopy; Russell-Saunders coupling; Term symbols and spectral details; origin of selection rules. Rotational, Vibrational, Electronic and Raman spectroscopy of diatomic and simple polyatomic molecules. Line broadening and line widths; simple properties of Gaussian and Lorentzian line shapes. Molecular spectroscopy: Absorbance, Beer- Lambert’s law, Einstein’s coefficient, Jablonski diagram. Relationship of transition moment integral with molar extinction coefficient and oscillator strength. Basic principles of Nuclear Magnetic Resonance: Gyromagnetic ratio; Chemical shift, nuclear coupling. · 2 marks · Numerical answer

A 532 nm laser Raman spectrometer records $Cl_2$ with fundamental vibration 560 cm$^{-1}$. The Stokes line is observed at ______ cm$^{-1}$ (nearest integer).

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Correct answer: 18225 to 18245

Explanation

The excitation wavenumber is 1/(532×10⁻⁷ cm)=18796.99 cm⁻¹. A Stokes photon loses one vibrational quantum, so subtract the Cl2 vibration: 18796.99−560=18236.99 cm⁻¹. Rounded to the nearest integer the line is **18237 cm⁻¹**. Anti-Stokes scattering would require addition instead.