Question

If the collision frequency of hydrogen molecules in a closed chamber at 27°C is \( Z \), then the collision frequency of the same system at 127°C is:

• A. \( \frac{\sqrt{3}}{2} Z \)
• B. \( \frac{4}{3} Z \)
• C. \( \frac{2}{\sqrt{3}} Z \)
• D. \( \frac{3}{4} Z \)

Answer 1

The Correct Option is C

If the mean free path is constant, the collision frequency \(f\) is directly proportional to the square root of temperature (\(\sqrt{T}\)):

\[ f \propto \sqrt{T} \]

Parameters:

\[ T_1 = 27^\circ C = 300 \, \text{K}, \quad T_2 = 127^\circ C = 400 \, \text{K} \]

The ratio of collision frequencies is calculated as:

\[ \frac{f_2}{f_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{400}{300}} = \sqrt{\frac{4}{3}} \]

Consequently:

\[ f_2 = \sqrt{\frac{4}{3}} \cdot f_1 = \frac{2}{\sqrt{3}} f_1 \]