GATE 2023 CY – Question 65

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

Three noninteracting compounds P,Q,R are in a cuvette of path 1 cm. Concentrations are $[P]=10^{-6}$ M, $[Q]=2\times10^{-6}$ M, $[R]=3\times10^{-6}$ M. Their molar extinction coefficients at 300 nm are $\epsilon_P=10^5$, $\epsilon_Q=2\times10^5$, $\epsilon_R=3\times10^5$ M$^{-1}$ cm$^{-1}$. Transmittance at 300 nm is ______ % (two decimal places).

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 3.98 to 4.00

Explanation

Absorbances add for noninteracting species: A=lΣ εici=1[(10⁵)(10⁻⁶)+(2×10⁵)(2×10⁻⁶)+(3×10⁵)(3×10⁻⁶)]=1.4. Transmittance fraction is 10^(−1.4), so percentT=100×10^(−1.4)=**3.98%** after rounding. Do not add transmittances directly.