Question

The temperature at which the r.m.s. velocity of oxygen molecule is equal to that of hydrogen molecule at 20 K is

• A. 300 K
• B. 320 K
• C. 330 K
• D. 400 K
• E. 375 K

Hint:

For equal rms velocity: \(T \propto M\).

Answer 1

The Correct Option is B

Concept: \[ v_{rms} = \sqrt{\frac{3kT}{M}} \Rightarrow v \propto \sqrt{\frac{T}{M}} \]

Step 1: Equate velocities.
\[ \frac{T_1}{M_1} = \frac{T_2}{M_2} \]

Step 2: Substitute values.
\[ \frac{T}{32} = \frac{20}{2} \]

Step 3: Solve.
\[ T = 20 \times \frac{32}{2} = 320 K \]