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The recoil speed of a hydrogen atom af...

The recoil speed of a hydrogen atom after it emits a photon is going form n=5 state to n =1 state is ….. m/s.

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From conservation of linear momentum, | Momentum of recoil hydrogen atom | = | Momentum of emitted photon |
or `mv = (Delta E)/(c )`
Here, `Delta E = E_5 - E_1 = - 13.6[(1)/(5^2) - (1)/(1^1)] eV`
`=(13.6)(24/25) eV = 13.056 eV`
`= 13.056xx1.6x10^(-19) J = 2.09x10^(-18) J` and `m= mass of hydrogen atom `=1.67xx10^(-27) kg` `:. v = (Delta E)/(mc) = (2.09xx10^(-18)/((1.67xx10^(-27) (3xx10^8)`
` v =4.17 m/s
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