Question

The average translational 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 (N = number of molecules, R = gas constant)

• A. \(\frac{eVN}{2R}\)
• B. \(\frac{2eVN}{3R}\)
• C. \(\frac{eVN}{R}\)
• D. \(\frac{3eVN}{4R}\)

Hint:

Average translational energy per molecule is (3/2) kT, with k = R/N.

Answer 1

The Correct Option is B

Step 1: Energies
$E_1 = \frac32\frac{R}{N}T$ and $E_2 = eV$.

Step 2: Equal
$\frac{3RT}{2N} = eV$.

Step 3: Solve
$T = \dfrac{2eVN}{3R}$. Option (B).

Final Answer:
Option (B). \[ \boxed{\frac{2eVN}{3R}} \]