The average translational energy and the rms speed of molecules in a sample of oxygen gas at `300K` are `6.21xx10^(-21)J` and `484m//s`, respectively. The corresponding values at `600K` are nearly (assuming ideal gas behaviour)

Options

A. `8.78xx10^(-21)J,684m//s`
B. `0.21xx10^(-21)J,989m//s`
C. `12.42xx10^(-21)J,684m//s`
D. `12.42xx10^(-21)J,968m//s`

Answer

C

Explanation

The average translation K.E.
`=1/2mv_("rms")^(2)=3/2KT=3/2(RT)/Ni.e.EpropT`
`thereforeE_(2)/E_(1)=T_(2)/T_(1)=2`
`thereforeE_(2)=2E_(1)=2xx6.21xx10^(-21)=12.42xx10^(-21)J`
Similarly `v_("rms")=sqrt((3RT)/m)orv_("rms")propsqrtT`
`((v_("rms"))_(2))/((v_("rms"))_(2))=sqrt(600/300)=sqrt2=1.414`
`therefore(v_("rms"))_(2)=1.414xx484=684m//s`