A photon with initial frquency `10^(11) `Hz scatters off an electron at rest. Its final frequency is `0.9xx10^(11)Hz`. The speed of scattered electron is close to :
`(h=6.63xx10^(-34)Js,m_(e)=9.1xx10^(-31)kg)`

Explanation

Incident energy = Scattered energy + K.E. of the scattered electron
`hv_(1) = hv_(2) + (1)/(2) mv^(2)`
or `(1)/(2) mv^(2) = h (v_(1) - v_(2))`
or `v^(2) = (2h(v_(1) - v_(2)))/(m) = (2 xx 6.63 xx 10^(-34) kg m^(2) s^(-1) (10^(11) - 0.9 xx 10^(11)) s^(-1))/(9.1 xx 10^(-31) kg)`
`= (2 xx 6.63 xx 10^(-34) xx 0.1 xx 10^(11))/(9.1 xx 10^(-31)) m^(2) s^(-2) = 14571428 m^(2) s^(-2)`
or `v = sqrt(14571428) ms^(-1) = 3.8 xx 10^(3) ms^(-1)`