A stream of electrons from a heated filament was passed between two charged plates

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

  1. 2meV
  2. √(meV)
  3. √(2meV)
  4. meV

Solution

According to de-broglie, the wavelength associated with a particle of mass m, moving with velocity v is given by the relation

\( \lambda = \dfrac{h}{mv} \)

Kinetic Energy = ½mv2 = eV

m2v2 = 2eVm

mv = √(2eVm)

\( \lambda = \dfrac{h}{\sqrt{2eVm}} \)

The correct option is C.