If e is the charge of an electron in esu m is the mass in grams and v the voltage 'h' is the planck constant in erg sec then the wavelength of the electron in cm is

Options

A. `h//sqrt(Ve)`
B. `hsqrt(Vme)`
C. `hsqrt(Ve)`
D. `hsqrt(2mVe)`

Answer

D

Explanation

Kinetic energy of electrons = Potential energy gained by each electron
i.e., 1/2 m `upsilon^2=eV` or `upsilon=sqrt((2eV)/m)`
`therefore lambda=h/(m upsilon)=h/(m((2eV)/m)^(1//2))=h/sqrt(2mVe)`