A hydrogen atom initally in the ground level absorbs aphoton, which excites it to be `n=4` level, Determine the wavelength and frequency of photon . To find the wavelength and frequency of photon use the relation of energy of electron in hydrogen atom is` E_(n)=-13.6/(n^(2)) eV`

Explanation

For ground state `n_(1)=1` to `n_(2)=4` .
Energy absorbed by photon , `E=E_(2)-E_(1)`
` =+13.6(1/n_(1)^(2)-1/n_(2)^(2))xx1.6xx10^(-19)J`
` =113.6(1/1-1/4^(2))xx1.6xx10^(-19)`
` = 13.6xx1.6xx10^(-19)(15/16)=20.4xx10^(-19)`
or `E=hv=20.4xx10^(-19)`
Freguency `v=(20.4xx10)^(-19)/h=(20.4xx10)^(-19)/(6.63xx10^(-34))`
` =3.076xx10^(15) Hz`.
Wavelength of photon `lambda=c/v=(3xx10^(8)/3.076xx10^(15))=`
` 9.74xx10^(-8)`, thus, the wavelength is `9.7xx10^(-8)m `
and frequency is` 3.1xx10^(15) Hz.