Answer
$9.6\times 10^{-5}m/s$
Work Step by Step
We can find the required rms speed as follows:
$v_{rms}=\sqrt{\frac{3k_B T}{\rho \frac{1}{6}\pi d^3}}$
$\implies v_{rms}=\sqrt{\frac{18k_B T}{\pi \rho d^3}}$
We plug in the known values to obtain:
$v_{rms}=\sqrt{\frac{18(1.38\times 10^{-23})(293)}{\pi (2500)(1\times 10^{-5})^3}}$
This simplifies to:
$v_{rms}=9.6\times 10^{-5}m/s$
