Question

Derive the expression for de-Broglie wavelength associated with an electron in a potential difference of V volts.

Answer 1

Let an electron having charge V and mass m be accelerated through a potential V volts, and attains a velocity v.

∴ Kinetic energy of electron,

E = \(\frac{1}{2}\) mv² ...........(i)

Also, kinetic energy of electron is given by

E = eV ............(ii)

From (i) and (ii), we have

\(\frac{1}{2}\) mv² = eV

or mv² = 2eV

or m²v² = 2 meV

or mv = \(\sqrt{2me V}\)

de-Broglie wavelength of electron,