Answer
(a) $640.03m/s$
(b) $3.48\times 10^{-8}m$
Work Step by Step
(a) We can find the required rms speed as follows:
$v_{rms}=\sqrt{\frac{3RT}{M}}$
We plug int the known values to obtain:
$v_{rms}=\sqrt{\frac{3\times 8.31\times 723}{44\times 10^{-3}}}$
This simplifies to:
$v_{rms}=640.03m/s$
(b) The mean free path can be determined as follows:
$\lambda=\frac{k_B T}{\sqrt{2} p d^2}$
We plug in the known values to obtain:
$\lambda=\frac{1.38\times 10^{-23}\times 723}{\sqrt{2}\pi \times 94.2\times 10^5(1.5\times 10^{-10})^2}$
This simplifies to:
$\lambda=3.48\times 10^{-8}m$
