The number of air molecules per increased from to . The ratio of collision frequency of air molecules before and after the increase in number respectively is [2023]

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Solution

Q.
The number of air molecules per ${cm}^{3}$ increased from $3 \times 10^{19}$ to $12 \times 10^{19}$ . The ratio of collision frequency of air molecules before and after the increase in number respectively is [2023]

1 0.75

2 0.50

3 0.25

4 1.25

Ans.
(3)

$Collision frequency,$

$f = \frac{V}{λ} = \frac{V}{(\frac{1}{\sqrt{2} π d^{2} n_{v}})} = \sqrt{2} π d^{2} v n_{v}$

$∴$ $f \propto n, n_{v} is number density$

$\frac{f_{1}}{f_{2}} = \frac{n_{v_{1}}}{n_{v_{2}}} = \frac{3 \times 10^{19}}{12 \times 10^{19}} = 0.25$

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