GATE 2021 CY – Question 55

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 400 nm deuterium lamp has power 1 μW. Its photons emitted per nanosecond number ______ (nearest integer). $h=6.626\times10^{-34}$ kg m$^2$ s$^{-1}$; $c=3.0\times10^8$ m/s.

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Correct answer: 2000 to 2020

Explanation

One photon has energy hc/λ=(6.626×10⁻³⁴×3.0×10⁸)/(400×10⁻⁹)=4.9695×10⁻¹⁹ J. In one nanosecond the lamp emits 10⁻⁶×10⁻⁹=10⁻¹⁵ J. Dividing gives 2012.27 photons/ns, or **2012** to the nearest integer. This assumes the stated output power is at 400 nm.