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GATE 2021 CY – Question 58

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 substance in cyclohexane has molar absorption coefficient 1710 L mol$^{-1}$ cm$^{-1}$ at 500 nm. For a 2 mmol/L solution in a 1 mm cell, the light-intensity reduction at that wavelength is ______ % (one decimal place).

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Correct answer: 54.0 to 55.0

Explanation

Convert the path length to 0.1 cm and concentration to 0.002 mol/L. Beer–Lambert absorbance is A=εcl=1710×0.002×0.1=0.342. Transmission is I/I0=10^(−0.342)≈0.4550.

Thus the percentage reduction is 100(1−0.4550)=**54.5%** to one decimal; absorbance itself is not a percentage.