Question

At what temperature is the R.M.S. velocity of a hydrogen molecule equal to that of an oxygen molecule at \(47^\circ\text{C}\)? (Molecular weight of hydrogen = 2, molecular weight of oxygen = 32)

• A. \(80\,\text{K}\)
• B. \(20\,\text{K}\)
• C. \(40\,\text{K}\)
• D. \(60\,\text{K}\)

Hint:

RMS velocity depends on the ratio \( \frac{T}{M} \), not on temperature alone.

Answer 1

The Correct Option is B

Step 1: Formula for RMS velocity.
\[ v_{\text{rms}} = \sqrt{\frac{3RT}{M}} \]

Step 2: Equate RMS velocities.
\[ \sqrt{\frac{T_H}{M_H}} = \sqrt{\frac{T_O}{M_O}} \]

Step 3: Substitute given values.
\[ \frac{T_H}{2} = \frac{(47+273)}{32} \] \[ T_H = \frac{320}{16} = 20\,\text{K} \]