Find the temperature at which the everage thermal kinetic energy is equal to the energy needed to take a hydrogen atom from its ground state `n = 3` state hydrogen can now emit rod light of wavelength `653.1 nm`because of maxwellan distribution of speeds a hydrogen sample emits red light at temperature much lower than that obtained from this problem Asuume that hydrogen that hydrogen molecules dissociate into atoms

Answer

A, D

Explanation

`K=8.62 xx 10^-5 eV//K`
K.E. of H_2 molecules `= 3/2 KT`
Energy released, when atom goes from ground state to `n=3`
`KE=13.6((1)/(1)-(1)/(9))`
`=3/2KT = 13.6((1)/(1)-(1)/(9))`
`3/2 xx 8.82 xx 10^-15T= (13.6 xx 6)/(9)`
`T=(13.6 xx 8 xx 2 xx 10)/(9 xx 3 xx 8.62)`
`=9.349 xx 10^5`
`=9.349 xx 10^4`
`=9.4 xx 10^4 K`