A hydrogen molecule $($diameter $1\mathrm{.}0108$ cm$),$ traveling at the rms speed, escapes from a $4600$ K furnace into a chamber containing cold argon atoms $($diameter $3\mathrm{.}0108$ cm$)$ at a density of $3\mathrm{.}61019$ atoms$/$cm$3.$

$($a$)$ What is the speed of the hydrogen molecule?

m$/$s

$($b$)$ If it collides with an argon atom, what is the closest their centers can be$,$ considering each as spherical?

cm

$($c$)$ What is the initial number of collisions per second experienced by the hydrogen molecule?

Hint:

Assume that the argon atoms are stationary. Then the mean free path of the hydrogen molecule is given by

$=$

$1$d$2$N$/$V

and not

$=$

$1$

$2$

$$d$2$N$/$V

$.$

collisions$/$s