IGNOU BPHCT 137 2026 - Two energy levels of an atomic system are separated by energy correspo

Question

Two energy levels of an atomic system are separated by energy corresponding to frequency $3.0 \times 10^{14}\text{ Hz}$ . Assume that all atoms are in one or the other of these two energy levels, compute the fraction of atoms in the upper energy level at temperature $400\text{ K}$ . Take $k_B = 1.38 \times 10^{-23}\text{ JK}^{-1}$ and $h = 6.6 \times 10^{-34}\text{ Js}$ .

19 Jan 2026

Answer :

Word Count : 252

We are asked to compute the fraction of atoms in the upper energy level using the Boltzmann distribution. Let’s solve step by step. The fraction of atoms in the upper energy level ( n_2 ) is given by: [ \frac{n_2}{n_1 + n_2} = \frac{1}{1 + \frac{n_1}{n_2}} = \frac{1}{1 + e^{\frac{E_2 - E_1}{k_B T}}} ] Here, ( E_2 - E_1 = h \nu ). Step 1: Calculate the energy difference [ E_2 - E_1 = h \nu = (6.6 \times 10^{-34}) \times (3.0 \times 10^{14}) \text{ J} ] Multiply carefully: 1. Multiply coefficients: ( 6.6 \times 3.0 = 19.8 ) 2. Multiply

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