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A stationary helium ion emits a photon c...

A stationary helium ion emits a photon corresponding to the first line of Lyman series. That photon liberates a photoelectron form a stationary hydrogen atom in ground state. Find the velocity of photoelectron. Take mass of electron `=9.11xx10^(-31)kg` and ionisation energy of hydrogen atom=13.6ev.

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for first line of Lyman series, `n_1=1, n_2=2` Energy of photon emitted by He atom (Z=2)
`DeltaE=13.6Z^2(1/(n_1^2)-1/(n_2^2))eV`
`=13.6xx2^2(1/(1^2)-1/(2^2))=40.8eV`
As ionisation energy of electron is 13.6eV.
`:.` KE of emitted photoelectron
`1/2mv^2=40.8-13.6=27.2ev`
`=27.2xx1.6xx10^(-19)"joule"`
`v=sqrt((2xx27.2xx1.6xx10^(-19))/(9.11xx10^(-31)))`
`v=3.1xx10^6m//s`
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