IGNOU BPHCT 135 2026 - N particles obey MB distribution. They are distributed among three sta

Question

N particles obey MB distribution. They are distributed among three states with energies $E_1 = 0, E_2 = k_BT$ and $E_3 = 3k_BT$ . If the equilibrium energy of the system is 2000 k_BT, calculate the total number of particles, N.

19 Jan 2026

Answer :

Word Count : 241

The problem gives a system of (N) particles obeying Maxwell–Boltzmann (MB) statistics, distributed among three energy states: [ E_1 = 0, \quad E_2 = k_B T, \quad E_3 = 3 k_B T ] The equilibrium energy of the system is (U = 2000, k_B T). We are asked to calculate (N). --- Step 1: Write the partition function (Z) for one particle [ Z = \sum_{i} e^{-E_i / k_B T} = e^0 + e^{-k_B T / k_B T} + e^{-3 k_B T / k_B T} = 1 + e^{-1} + e^{-3} ]

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