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 the photon before collison `= hv = (hc)/(lamda)`
Energy of the photon after collision `= hv' = (hc)/(lamda')`
Difference of energy is imparted to the electron.
Hence, energy of the scattered electron `= (hc)/(lamda) - (hc)/(lamda') = hc ((1)/(lamda)- (1)/(lamda'))`
`= (6.626 xx 10^(-34) J s) (3 xx 10^(8) m s^(-1)) xx ((1)/(1.4 xx 10^(-10)m) - (1)/(2.0 xx 10^(-10) m))`
`= (6.626 xx 10^(-34)Js) (3 xx 10^(8) ms^(-1)) xx ((2.0 - 1.4) xx 10^(-10) m^(-1))/((1.4 xx 10^(-10)) (2.0 xx 10^(-10))) = 4.26 xx 10^(-16) J`