IGNOU PHE 9 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 × 10¹⁴ 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 K. Take k_B = 1.38 × 10⁻²³ JK⁻¹ and h = 6.6 × 10⁻³⁴ Js.

28 Jan 2026

Answer :

Word Count : 411

In an atomic system having only two energy levels, the population of atoms in each level at thermal equilibrium is governed by the Boltzmann distribution. The separation between the two energy levels is given in terms of the corresponding radiation frequency as 3.0 × 10¹⁴ Hz. The energy difference between the upper and lower levels is therefore obtained using the Planck relation ΔE = hν. Substituting the given values of Planck’s constant and frequency, the energy separation becomes ΔE = (6.6 × 10⁻³⁴ Js) × (3.0 × 10¹⁴ Hz) = 1.98 × 10⁻¹⁹ J. At a temperature of 400 K, the thermal energy available to the atoms is measured by kBT, where kB is the Boltzmann constant. Using the given value of kB, the thermal energy is kBT = (1.38 × 10⁻²³ JK⁻¹) × 400 = 5.52 × 10⁻²¹ J. The ratio of the population of atoms in the upper energy level (N₂) to that in

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