If an electron and a proton have the same de - Broglie wavelength , then the kinetic energy of the electron is

Options

A. more than that of a proton
B. equal to that of a proton
C. zero
D. less than that of a proton

Answer

A

Explanation

`lambda_("de Broglie")=h//p`
`therefore` As the wavelength are the same , `(h)/(m_(e)v_(1))=(h)/(m_(p)*v_(2))`
`rArrm_(e)v_(1)=m_(p)*v_(2)`.
Kinetic energy of the electron `=(1)/(2m_(e))(m_(e)v_(1))^(2)`
Kinetic energy of the proton `=(1)/(2m_(p))(m_(p)v_(2))^(2)`.
Therefore yhe kinetic energy of electron is about 2000 times more than than of the proton as the proton is about 2000 times heavier than the electron.