The number of gas molecules striking per second per square metre of the top surface of a table placed in a room at $20^{\circ} C$ and 1 atmospheric pressure is of the order of $\left(k_{B}=1.4 \times 10^{-23} \,JK ^{-1}\right.$ and the average mass of an air molecule is $5 \times 10^{-27} \,kg$ )
A$10^{27}$
B$10^{23}$
C$10^{25}$
D$10^{29}$
KVPY 2017, Diffcult
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A$10^{27}$
a $(a)$ Using, $v_{ rms }=\sqrt{\frac{3 k T}{m}}$ and $\quad p=N \times 2 m v_{\text {rms }}$
We have,
$N=\frac{p}{2 m} \frac{p}{v_{\text {rms }}}=\frac{p \times \sqrt{m}}{2 m \cdot \sqrt{3 k T}}=\frac{(p / 2)}{\sqrt{3 m k T}}$
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