Find the wavelength present in the radiation emitted when hydrogen atoms emitted to `n = 3` states return to their ground state.

Explanation

A hydrogen atom may return direction to the ground or it may go to `n = 2` and from there to the ground state Thus , wavelength corresponding to `n = 3 rarr n = 1, n= 3 rarr n= 2 and n = 2 rarr n = 1` are ground in the radition
The energies in `n = 1`, `2 and 3` states are
`E_(1) = -13.6 eV`
`E_(2) = (13.6)/(4) eV = -3.4 eV`
`and E_(3) = (13.6)/(9)eV = - 1.5eV`
the wavelength emitted in the transition `n = 3` to the ground state is
`lambda = (hc)/(Delta E)`
`= (1242eV nm)/(13.6- 1.5eV)= 105nm`
Similarly the wavelength emitted in the transition `n = 3 to n = 2 is 654 nm` and that emitted in the transition `n = 2 to n= 1 is 132nm` The wavelength p-resent in the radition are therefore `103nm , 122nm and 654nm`