Question

Calculate the
(a) momentum, and
(b) de Broglie wavelength of the electrons accelerated through a potential difference of 56 V.

Answer 1

Potential difference, V = 56 V
Planck’s constant, h = 6.6 × 10⁻³⁴ Js
Mass of an electron, m = 9.1 × 10⁻³¹ kg
Charge on an electron, e = 1.6 × 10⁻¹⁹ C
(a) At equilibrium, the kinetic energy of each electron is equal to the accelerating
potential, i.e., we can write the relation for velocity (v) of each electron as:

The momentum of each accelerated electron is given as:
p = mv
= 9.1 × 10⁻³¹ × 4.44 × 10⁶
= 4.04 × 10⁻²⁴ kg m s⁻¹

Therefore, the momentum of each electron is 4.04 × 10⁻²⁴ kg m s^−1
.
(b) De Broglie wavelength of an electron accelerating through a potential V, is given by
the relation:

Therefore, the de Broglie wavelength of each electron is 0.1639 nm.