Calculate the rms speed , average speed and the most probable speed of 1 mole of hydrogen molecules at 300K . Neglect the mass of electron.

Explanation

The hydrogen atom has one proton and one electron. The mass of electron is negligible compared to the mass of proton `=1.67xx10^(-27)` kg
One hydrogen molecule =2 hydrogen atoms `=2xx167xx10^(-27)` kg
The average speed `barnu=sqrt((8kT)/(pim))=1.60sqrt((kT)/m)`
`=1.60sqrt(((1.38xx10^(-13))xx(300))/(2(1.67xx10^(-27))))=178xx10^(3)ms^(-1)`
(Boltzmann Constant `k=1.38xx10^(-32)JK^(-1)`)
The rms speed `nu_(rms)=sqrt((3kT)/m)=1.73sqrt((kT)/m)`
`=1.73sqrt(((1.38xx10^(-23))xx(300))/(2(1.67xx10^(-27))))=1.93xx10^(3)ms^(-1)`
Most probable speed `nu_(mp)=sqrt((2kT)/m)=1.41sqrt((kT)/m)`
`=1.41sqrt(((1.38xx10^(-23))xx(300))/(2(1.67xx10^(-27))))=1.57xx10^(3)ms^(-1)`
Note that `nu_(rms) gt barnu gt nu_(mp)`