Knudsen diffusion is a phenomenon whereby transport takes place by gas-pore wall collisions rather than by gas-gas collisions. Knudsen diffusion is modeled using concepts similar to the kinetic theory of gases as \(D_{\mathrm{KA}}=\left(d_{\mathrm{p}} / 3\right) \bar{c}\), where \(\bar{c}\) means the molecular velocity given earlier in Eq. (1.37). Use this to derive the following equation for the Knudsen diffusion coefficient:

\[\begin{equation*}D_{\mathrm{KA}}=4850 d_{\mathrm{p}} \sqrt{\frac{T}{M_{\mathrm{A}}}} \tag{9.61}\end{equation*}\]

Calculate the value for silane diffusing in \(10-\mu \mathrm{m}\)-diameter pores at \(900 \mathrm{~K}\), which is representative of the deposition of solid silicon in thin tubes.

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= 8KT T M (1.37)