Question

An electron is accelerated through a potential difference of 100 V.

a. What is the velocity of the electron?

v = _______ x10 ⁶ m/s

b. What is the momentum of the electron?

p = _______ x10 ^-24 kg m/s

c. What is the de Broglie wavelength of the electron?

λ = _______ nm

Answer 1

a)
Equating potential energy with the kinetic energy,
e * V = 1/2 * m * v²
Where e, m and V are the charge, mass and velocity of electron, V is the potential difference.
v² = (2 * e * V) / m
v = SQRT[(2 * e * V) / m]
Substituting values,
v = SQRT[(2 * 1.6 * 10^-19 * 100) / (9.11 * 10^-31)]
= SQRT[36.13 * 10¹²]
= 5.93 * 10⁶ m/s

b)
Momentum, p = m * v
= (9.11 * 10^-31) * (5.93 * 10⁶)
= 5.40 * 10^-24 kg.m/s

c)
de Broglie wavelength, = h / p
Where h is the Planck's constant and p is the momentum.
= (6.63 * 10^-34) / (5.40 * 10^-24)
= 1.23 * 10^-10
= 0.123 * 10^-9 m
= 0.123 nm