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 each particle,
`lamda=1nm=1xx10^(-9)m`
(i) Both electron and photon will have equal momentum as
`p=h/lamda=(6.63xx10^(-34))/(1xx10^(-9))=6.63xx10^(-25)"kg m s "^(-1)`
(ii) Energy of a photon is
`E=(hc)/lamda=(6.63xx10^(-34)xx3xx10^8)/(1xx10^(-9))`
`=19.89xx10^(-17)J`
`=(19.89xx10^(-17))/(1.6xx10^(-19))eV=12.44xx10^2eV`
(iii) Kinetic energy of the electron is
`K=p^2/(2m_e)=((6.63xx10^(-25))^2)/(2xx9.1xx10^(-31))J`
`=2.415xx10^(-19)J`
`=(2.415xx10^(-19))/(1.6xx10^(-19))eV`
`=1.51eV`