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(B) The collision frequency $(Z)$ is given by the formula: $Z = \sqrt{2} \pi d^2 N \bar{v}$,where $\bar{v} = \sqrt{\frac{8RT}{\pi M}}$.Since temperatu

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$4 	imes 10^{18}$

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(B) The collision frequency $(Z)$ is given by the formula: $Z = \sqrt{2} \pi d^2 N \bar{v}$,where $\bar{v} = \sqrt{\frac{8RT}{\pi M}}$.Since temperature $(T)$ and number density $(N)$ are the same for both gases,we have $Z \propto d^2 \sqrt{\frac{1}{M}}$.Given: $d_A = \frac{d_B}{2}$ and $M_A = 4M_B$.Therefore,the ratio of collision frequencies is:$\frac{Z_A}{Z_B} = \left( \frac{d_A}{d_B} ight)^2 \sqrt{\frac{M_B}{M_A}}$$\frac{Z_A}{Z_B} = \left( \frac{1}{2} ight)^2 \sqrt{\frac{M_B}{4M_B}} = \frac{1}{4} 	imes \frac{1}{2} = \frac{1}{8}$.Given $Z_B = 32 	imes 10^{18} /s$,we get:$Z_A = \frac{32 	imes 10^{18}}{8} = 4 	imes 10^{18} /s$.

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