Question

calculate the most probable speed, average speed and the root mean square speed for gas molecules at 300 K . the mass of the gas molecules is 5 * $10^{-26}$ kg and Kb = 1.38 * $10^{-23}$ $JK^{-1}$

Answer 1

most probable speed =√(2kT)/m

where k is boltzman constant , T is temperature and m is the mass of gas molecule .

so,
Most probable speed = √{ 2 x 1.38 x 300 x 10^-23/5 x 10^-26}

= √(2 x 1.38 x 300 x 10³/5 } m/s

= √(12 x 1.38) x 10² m/s

in this way
average speed = √(8kT/m)
and
Root mean square speed =√(3kT/m)
put m, k , T value and find