Question

Calculate the de- Broglie wavelength of electron accelerated through 100 volt

Answer 1

We have the kinetic energy of an electron accelerated through a potential difference of V volts is given by the equation:

E_k = 1/2mv² = eV where e is the electron charge (1.6x10^-19 C)

The mass of an electron = 9.11 x 10^-31 kg

and so v = √(2eV/m) = √(2x1.6x10^-19x100/9.11 x 10^-31) = 5.92x10⁶ m/s 

Therefore: wavelength = h/mv = h/[9.11x10^{- 31}x5.92x10⁶]

 = 6.63x10^-34/[9.11x10^{- 31}x5.92x10⁶]

= 0.12 x 10^-9 m