a
\(v=\frac{V_{a v}}{\lambda}\)

\(\lambda=\frac{\mathrm{RT}}{\sqrt{2} \pi \sigma^{2} \mathrm{N}_{\mathrm{A}} \mathrm{P}}\)

\(\sigma=2 \times 0.3 \times 10^{-9}\)

\(P=\frac{R T}{V}\)

\(\Rightarrow \quad=\frac{V}{\sqrt{2} \pi \sigma^{2} N_{A}}\)

\(V_{\mathrm{av}}=\sqrt{\frac{8}{3 \pi}} \times V_{\mathrm{rms}}\)

\(\begin{aligned} \therefore \quad \mathrm{v} =\frac{200 \times \sqrt{2} \pi \times \sigma^{2} \mathrm{N}_{\mathrm{A}}}{25 \times 10^{-3}} \times \sqrt{\frac{8}{3 \pi}} \\ =17.68 \times 10^{8} / \mathrm{sec} \\ =0.1768 \times 10^{10} / \mathrm{sec}-10^{10} \end{aligned}\)

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