A hydrogen atom initially in the ground level absorbs a photon , which excites it to then `n=4` level. Determine the wavelength and frequency of photon.

Explanation

The energy of electron in `n^(th)` state of hydrogen atom is given by :
`E_n=-13.6/n^2`
So energies in `1^(st)` and `4^(th)` states will be :
`E_1`=-13.6 eV and `E_4=-13.6/4^2` =-0.85 eV
`therefore` Energy absorbed during excitation
`E=E_4-E_1`=-0.85+13.6
=12.75 eV
Let v be the frequency of absorbed photon. Then
hv=E=12.75 eV `=12.75xx1.6xx10^(-9)` J
`therefore v=(12.75xx1.6xx10^(-19))/(6.63xx10^(-34))`
`=3.076xx10^15` Hz
`approx 3.1xx10^15` Hz
Wavelength is given by
`lambda=c/v=(3xx10^8)/(3.076xx10^15)`
`=975xx10^(-10)` m
`approx 9.75xx10^(-8)` m