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

Explanation

For ground state `n_(1)=1 and n_(2)=4`
Energy of photon absorbed `E=E_(2)-E_(1)`
`=(-13.6)/(n_(2)^(2))-((-13.6)/(n_(1)^(2)))eV=13.6 ((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
`=13.6 ((1)/(1^(2))-(1)/(4^(2)))eV`
`=13.6xx(15)/(16) eV =(13.6xx15)/(16)xx1.6xx10^(-19) J`
`E=2.04xx10^(-18)` Joule.
From `E=(hc)/(lamda), lamda =(hc)/(E)=(6.6xx10^(-34)xx3xx10^(-8))/(2.04xx10^(-10))=9.7xx10^(-8) m`
`lamda =97 nm`
`v=(c)/(lamda)=(3xx10^(8))/(9.7xx10^(-8))=3.1xx10^(15) Hz.`