If `E_(1) , E_(2) "and" E_(3)` represent respectively the kinetic energies of an electron , an alpha particle and a proton each having same de Broglie wavelength then :

Options

A. `E_(1) gt E_(2) gt E_(3)`
B. `E_(3) gt E_(2) gt E_(1)`
C. `E_(1) gt E_(3) gt E_(2)`
D. `E_(1) = E_(2) = E_(3)`

Answer

C

Explanation

`K.E. = (1)/(2) mv^(2) and lamda = (h)/(mv) or v = (h)/(m lamda)`
`:. K.E. = (1)/(2) m (h^(2))/(m^(2) lamda^(2)) = (h^(2))/(2m lamda^(2))`
As `lamda` is same for given particles, `E prop (1)/(m)`
But `m_(e) lt m_(H^(+)) lt m_(alpha)`
Hence, `E_(1) gt E_(3) gt E_(2)`