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 :

Solution

Physics sir · 4 steps

Closed chamber fixes the mean free path, so only speed changes, and speed goes as √T.

1. Collision frequency. A molecule collides once every mean free path, so Z = v̄/λ. Here v̄ is the average speed and λ = 1/(√2 π d² n) is the mean free path.
2. What stays fixed. The chamber is closed, so the number of molecules per unit volume n does not change. The molecular diameter d is also fixed, so λ is the same at both temperatures.
3. What changes. The average speed is v̄ = √(8RT/(π M)), so v̄ ∝ √T. That makes Z ∝ √T, with T in kelvin: T₁ = 300 K and T₂ = 400 K.

   Z₂/Z = √(T₂/T₁) = √(400/300) = 2/√3

4. So. The new collision frequency is 2/√3Z, which is option (b).

The idea to keep. In a closed, fixed-volume gas the mean free path does not depend on temperature. Collision frequency then follows the speed, so Z ∝ √T. Always convert to kelvin first.

Answer from the NTA final answer key. Solution by PrepWiser.