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Question

$$Rms$$ speed of $$O_2$$ molecule is $$200 \,m/s$$ at $$T = 300 \,K$$ and $$P = 3atm$$. If diameter of molecule is $$0.3 \,nm$$ then collision frequency is:


A
2.9×107s1
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B
2.9×106s1
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C
2.9×108
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D
2.9×105
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Solution

The correct option is B $$2.9 \times 10^7 s^{-1}$$
Collision frequency $$= \sqrt{\dfrac{8 kT}{\pi m}} . \dfrac{\sqrt{2} \pi d^2 N_A P}{RT}$$
$$= \sqrt{\dfrac{8}{\pi} \times \dfrac{25}{3} . \dfrac{300}{32}} \dfrac{\sqrt{2 \pi} \times 9 \times 10^{-29} \times 6.023 \times 10^{23} \times 10^5}{\dfrac{25}{3} \times 300} = \dfrac{722. \, 14}{25} \times 10^6$$
$$= 28.8 \times 10^6 = 2.9 \times 10^7 s^{-1}$$

Physics

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