GATE 2021 CY – Question 59

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

The fundamental vibration of $\!{}^1H{}^{127}I$ is 2309 cm$^{-1}$. Its force constant is ______ N/m (nearest integer). $N_A=6.022\times10^{23}$; $c=3.0\times10^8$ m/s.

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Correct answer: 309 to 315

Explanation

For a harmonic diatomic oscillator, k=4π²c²ν̃²μ. The reduced mass is μ=[1×127/(1+127)]×10⁻³/(6.022×10²³) kg. Convert ν̃ to 230900 m⁻¹ and use c=3.0×10⁸ m/s. Substitution gives k≈312.11 N/m, or **312 N/m** to the nearest integer.