An electron and a photon each have a wavelength 1.00 nm. Find
(i) their momenta,
(ii) the energy of the photon and
(iii) the kinetic energy of electron.

Explanation

Given , wavelength of electron or a photon,
`lamda_(ph) =lamda_3=lamda=1.00 nm = 10^(-9)m`
(a) Momentum is equal for both particles and is given by
`p=p_(ph)=p_e=h/lamda=(6.62xx10^(-34))/(10^(-9))`
`=6.62xx10^(-25) "kg m s "^(-1)`
(b) Energy of photon is
`E_(ph) =pc = 6.62 xx10^(-25)xx3xx10^(-8)`
`=19.89xx10^(-17)J`
`=(19.89xx10^(-17))/(1.6xx10^(-19))eV`
`=1.243xx10^3eV=1243keV`
(c) Kinetic energy of electron is
`E_e=p_e^2/(2m)=(6.62xx6.62xx10^(-50))/(2xx9.1xx10^(-31))`
`=2.41xx10^(-19)J`
`=(2.41xx10^(-19))/(1.6xx10^(-19))=1.51eV.`