An electron and a photon each have a wavelength of 1.00 nm. Find
a. their momenta,
b. the energy of the photon, and
c. the kinetic energy of electron.

Explanation

(a) Both electron and photon have same wavelength. So, they have same momentum also,
`P = (h)/(lambda) = (6.6 xx 10^(-34))/(1 xx 10^(-9)) = 6.6 xx 10^(-25) "kg ms"^(-1)`
(b) Energy of a photon,
`E = (hc)/(lambda) = (6.6 xx 10^(-34) xx 3 xx 10^(8))/(1 xx 10^(-9)) = 19.8 xx 10^(-17)J`
`= (19.8 xx 10^(-17))/(1.6 xx 10^(-19)) = 12.375 xx 10^(2) = 1.24 xx 10^(3) eV`
E = 1.24 keV
(c) Kinetic energy of electron,
`K = (p^(2))/(2m)`
`= ((6.6 xx 10^(-25))^(2))/(2 xx 9.1 xx 10^(-31)) = (43.56 xx 10^(-50))/(18.2 xx 10^(-31)) = 2.39 xx 10^(-19) J`
`= (2.39 xx 10^(-19))/(1.6 xx 10^(-19))`
K = 1.49 eV