Q114 / 150 · MHT CET 2021 (23 Sep Shift 1) · Physics

At what temperature does the average translational kinetic energy of a molecule in a gas becomes equal to kinetic energy of an electron accelerated from rest through potential difference of ' $\mathrm{V}$ ' volt? ( $\mathrm{N}=$ Avogadro number, $\mathrm{R}$ = gas constant, $\mathrm{e}=$ electronic charge $)$

  • Correct answer
    A
    $\frac{2 \mathrm{eVN}}{3 \mathrm{R}}$
  • B
    $\frac{\mathrm{eVN}}{\mathrm{R}}$
  • C
    $\frac{\mathrm{eVN}}{4 \mathrm{R}}$
  • D
    $\frac{3 \mathrm{eVN}}{2 \mathrm{R}}$

Solution

The average translational kinetic energy of a gas molecule $=\frac{3}{2} \mathrm{kT}=\frac{3}{2} \frac{\mathrm{R}}{\mathrm{N}} \mathrm{T}$ The kinetic energy of a electrons accelerated by a p.d. of V volts $$ \begin{aligned} & =\mathrm{eV} \\ & \therefore \frac{3}{2} \frac{\mathrm{RT}}{\mathrm{N}}=\mathrm{eV} \\ & \therefore \mathrm{T}=\frac{2 \mathrm{eVN}}{3 \mathrm{R}} \end{aligned} $$

Hence, the correct answer is option: 'A'.

Relevant Questions