Answer
a) $v_{rms}=461\frac{m}{s}$
b) $f=27\frac{rounds}{s}$
Work Step by Step
a) $v_{rms}=\sqrt{\frac{3kT}{m}}=\sqrt{\frac{3(1.38\times10^{-23}\frac{J}{K})(273K)}{32\times1.66\times10^{-27}kg}}=461\frac{m}{s}$
b) $v_{rms}^2=v_x^2+v_y^2+v_z^2=3v_x^2$
$v_x=\frac{v_{rms}}{\sqrt{3}}$
$t_{bf}=\frac{2d}{v}=\frac{10m}{\frac{461\frac{m}{s}}{\sqrt{3}}}=0.0375s$
$f=\frac{1}{0.0375s}=27\frac{rounds}{s}$
