A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu. If c and m are charge and mass of an electron repectively, then the value of `h//lambda` (where `lambda` is wavelength associated with electron wave) is given by :

Options

A. `me V`
B. `2 me V`
C. `sqrt(me V)`
D. `sqrt(2 me V)`

Answer

D

Explanation

An electron of charge .e. is passed through a potential difference of V, then its kinetic energy becomes eV.
`1/2 mv^2 = eV`
or `" " v = sqrt((2eV)/(m))`
According to de-Broglie,
`lambda = h/(mv) = h/(msqrt((2eV)/(m)))`
or `" " lambda = h/(sqrt(2m eV))`
`:. h/lambda = sqrt(2 m eV)` .