Kinetic Theory

JEE Main level, single correct, medium

11 of 168

Question 11 of 168

The number of air molecules per cm3{cm}^{3} is increased from 3×10193\times {10}^{19} to 12×1019.12\times {10}^{19}. The ratio of collision frequency of air molecules before and after the increase in number respectively is :

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Answer: (D) 0.250.25

The given data is
n1=3×1019n2=12×1019{n}_{1}=3\times {10}^{19} {n}_{2}=12\times {10}^{19}
The mean time between two collision has the meaning of a period τ\tau, since it indicates the repetitive time intervals in which on average collisions take place. The reciprocal of the time τ\tau can be understood as the collision frequencyff, which indicates the number of collisions per unit time.The collision frequency is also directly proportional to the number molecules per unit volume.
f∝1τf\propto \dfrac{1}{\tau }
⇒f∝n\Rightarrow f\propto n
⇒f1f2=n1n2=3×101912×1019=0.25\Rightarrow \dfrac{{f}_{\text{1}}}{{f}_{\text{2}}}=\dfrac{{n}_{1}}{{n}_{2}}=\dfrac{3\times {10}^{19}}{12\times {10}^{19}}=0.25

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