GATE 2026 CY – Question 31

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. · 1 mark · Numerical answer

A 0.005 M solution of X transmits 80% of incident 500 nm light over path length 1.0 cm. The absorbance of a 0.01 M solution (three decimal places) is _____

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Correct answer: 0.184 to 0.204

Explanation

**Beer-Lambert law:** $A=\varepsilon\,c\,\ell$, so for the same path length and wavelength the absorbance is proportional to the concentration.

**Absorbance of the 0.005 M solution** (transmittance $T=0.80$):
$$A_1=-\log_{10}T=-\log_{10}0.80=0.09691 .$$

**Doubling the concentration** (0.01 M) doubles the absorbance:
$$A_2=2\times0.09691=\mathbf{0.194}.$$