The wavelength of a photon is `1.4 Å`. It collides with an electron. Its wavelength after collision is `2.0 Å`. Calculate the energy of the scattered electron.

Explanation

Energy of photon before collision `hv=(hc)/(lambda)`
Energy of photon after collision`=hv'=(hc)/(lambda')`.
Difference in the energies is that of the energy of the scattered electron.
`:. " "` Energy of the scattered electron `=(hc)/(lambda)-(hc)/(lambda')=hc((1)/(lambda)-(1)/(lambda'))`
`lambda=1.4Ã…=1.4xx10^(-10)m , lambda'=2.0xx10^(-10)m`,
`c=3xx10^(8)m s^(-1), h=6.626xx10^(-34)Js`.
`:.` Energy of the scattered electron =`(6.626xx10^(-34)Js)xx(3xx10^(8)ms^(-1))xx((1)/(1.4xx10^(-10)m)-(1)/(2.0xx10^(-10)m))`
`=((6.626xx10^(-34)Js)xx(3xx10^(8)ms^(-1))xx(2.0-1.4)xx10^(-10))/((1.4xx10^(-10))xx(2.0xx10^(-10)m))`
`=4.26xx10^(-16)J`.