Calculate the KE per molecule and also rms velocity of a gas at `127^(@)C`. Given `k = 1.38 xx 10^(-23) J "molecule"^(-1) K^(-1)` and mass of each molecule `= 6.4 xx 10^(-27) kg`.

Answer

`8.28 xx 10^(-21)J`; 1.61 xx 10^(3)m//s`

Explanation

Here,`T = 127^(@)C = (127+273)K = 400K`
`K = 1.38 xx 10^(-23) J "molecule"^(-1) K^(-1)`
`m= 6.4 xx 10^(-27) kg`
KE per molecule
`=3/2 kT = 3/2 xx 1.38 xx 10^(-23) xx 400`
`=8.28 xx 10^(-21)J`
As `KE = 1/2 mc^(2)`
`:. C = sqrt((2KE)/(m)) = sqrt((2 xx 8.28 xx 10^(-21))/(6.4 xx 10^(-27)))`
`=1.61 xx 10^(3)m//s`