The average transnational kinetic energy of a molecule in a gas is E₁. The kinetic energy of the electron (e) accelerated from rest through potential difference 'V' volt is E₂. The temperature at which E₁ = E₂ possible is (mass of molecule and electron is same) (N = number of molecules, V = Velocity, R = gas constant) (a) (2VNe)/(3R) (b) VNe/2R (c) (3NeV)/(2R) (d) (5NeV)/(3R)

Answer: (a). Average translational KE per molecule: E₁ = 3/2kT = 3RT/2N (using k = R/N). Electron accelerated through V: E₂ = eV. 3RT/2N = eV ⇒ T = (2NeV)/(3R) So the answer is (a) (2VNe)/(3R).

The average transnational kinetic energy of a molecule in a gas is… | MHT CET 2026 (16 Apr, Shift 2)

Q9MHT CET 2026 · 16 APR · SHIFT 2Difficult

Molecular Speeds & Maxwell Distribution

The average transnational kinetic energy of a molecule in a gas is $E_1$ . The kinetic energy of the electron (e) accelerated from rest through potential difference 'V' volt is $E_2$ . The temperature at which $E_1 = E_2$ possible is (mass of molecule and electron is same) (N = number of molecules, V = Velocity, R = gas constant)

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Answer: (a)

Average translational KE per molecule: $E_1 = \dfrac{3}{2}kT = \dfrac{3RT}{2N}$ (using $k = R/N$ ).
Electron accelerated through $V$ : $E_2 = eV$ .
$\dfrac{3RT}{2N} = eV \Rightarrow T = \dfrac{2NeV}{3R}$
So the answer is (a) $\dfrac{2VNe}{3R}$ .

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Molecular Speeds & Maxwell Distribution question from MHT CET 2026 (16 Apr, Shift 2)

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