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_(1) = 5 and n_(1) = 2 `, this transition gives rise to a spectral line in the visible region of the balmer series. From equation
`DeltaE=2.18xx10^(-18)J[1/5^(2)-1/2^(2)]`
` 4.58xx 10^(-19)J`
it is an emission energy
the frequency of the photon ( taking energy in terms of magnitude ) is given by
`v=(DeltaE)/h`
`( 4.58xx10^(-19)J)/(6.626xx10^(-34) Js)`
`6.91xx10^(14)Hz`
` lambda=c/v= (3.0xx10^(8)m s^(-1))/(6.91xx10^(14)Hz)=434 nm`