What is the minimum energy that must be given to a H atom in ground state so that it can emit an `H_(gamma)` line in Balmer series? If the angular momentum of the system is conserved, what would be the angular momentum of such `H_(gamma)` photon ?

Explanation

For Balmer series of atomic spectrum of hydrogen,
`(1)/(lambda)=R((1)/(2^(2))-(1)/(n^(2)))`
where `n=3,4,5,6,....oo` respectively for `H_(alpha) , H_(beta), H_(gamma), H_(delta),....H_(oo)` lines ).
Here for `H_(gamma)` lines n=5 and so minimum energy to be supplied to an electron lying in n = 1 energy level will be equal to,
`E_(5)-E_(1)=-(13.6)/(n^(2))-(13.6)`
`=13.6-(13.6)/(n^(2))`
`=13.6-(13.6)/(n^(2))`
`=13.6-(13.6)/((5)^(2))( :.n=5)`
`=13.6(1-(1)/(25))`
`=(13.6xx24)/(25)`
`=13.056eV`
Angular momentum of emitted `H_(gamma)` photon,
= decrease in angular momentum of electron
`=l_(5)-l_(2)`
`=(5h)/(2pi)-(2h)/(2pi)`
`=(3h)/(2pi)`
`=(3xx6.625xx10^(-34))/(2xx3.14)`
`=3.165xx10^(-34)Js`