The number of air molecules per cm³ increased from 3 × 10¹⁹ to 12 × 10¹⁹. The ratio of collision frequency of air molecules before and after the increase in the number respectively is:
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Question

The number of air molecules per cm³ increased from 3 × 10¹⁹ to 12 × 10¹⁹. The ratio of collision frequency of air molecules before and after the increase in the number respectively is:

G1 Physics · Accepted Answer

Collision frequency for gas molecules is proportional to number density when temperature and molecular size remain unchanged: f ∝ n Initially: n₁ = 3 × 10¹⁹ cm⁻³ Finally: n₂ = 12 × 10¹⁹ cm⁻³ Therefore, f₁/f₂ = n₁/n₂ = 3/12 = 1/4 = 0.25 Hence option A follows.