what are the frequency and wavelength of a photon emitted during a transition from n = 5 state to the n =2 state in the hydrogen atom?

Explanation

Since `n_i = 5 and n_f = 2` , this transition gives rise to a special line in the visible region of the Balmer series.
`Delta E = 2.18 xx 10^(-18) J [ (1)/(5^(2)) - (1)/(2^(2))]= -4.58 xx 10^(-19) J`
The frequency of the photon (taking energy in terms of magnitude) is given by
`v = (Delta E)/(h ) = (4.58 xx 10^(-19) J )/(6.626 xx 10^(-34) Js) = 6.91 xx 10^(14)` Hz
`lambda= (c )/ (v) = (3.0 xx 10^(8) ms^(-1))/(6.91 xx 10^(14) Hz) = 434 nm`