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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 ?

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High energy level n=4 so `n_(i) =4` (initial )
for hydrogen z=1
`Delta E =2.18 xx 10^(18) ((1)/(n_(1)^(2))-(1)/(n_(f)^(2)))`
`=2.18 xx 10^(18) ((1-4)/(16))J`
`=4.0875 xx 10^(19) J`
`=((6.626 xx 10^(34) J s ) (3.0 xx 10^(8) m))/( 4. 0 875 xx 10^(19) J)`
`=4.8631 xx 10^(7) n xx 10^(9) nm`
`=486 .31 nm`
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