Find the ratio of energies of photons produced due to transition of electron of hydrogen atom form its (i) second permitted energy level to the first level (ii) highest permitted energy level to the first permitted level.

Explanation

(i) `because " " E_(n) = ( - 13.6)/(n^(2)) eV`
`therefore " " E_(1) = (-13.6)/((1)^(2)) = -13.6 eV`,
`E_(2) (-13.6)/((2)^(2)) = -3.4 eV therefore (E_(2))/(E_(1)) = (-3.4)/(-13.6) = (1)/(4) therefore E_(2) : E_(1) = 1 : 4`.
(ii) `" " E_(1) = (-13.6)/((1)^(2)) , E_(7) = (-13.6)/((7)^(2)) therefore (E_(7))/(E_(1)) = (-13.6)/((7)^(2)) xx ((1)^(2))/(-13.6) = (1)/(49) = 1 : 49`.