Question

A beam of electrons with kinetic energy 25 eV encounter a potential barrier of height 20 eV. Some electrons reflect from the barrier, and some are transmitted. Find the wave number k of the transmitted electrons.

You can take U = 0 for x < 0, and U = 15 eV for x > 0

Answer 1

The wave number of a transmitted electrons which will be given by -

k = 2 m (E - V₀) / (hbar)²

where, m = mass of electron = 9.11 x 10^-31 kg

V₀ = potential barrier = 20 eV = 3.2044 x 10^-18 J

E = kinetic energy of electron = 25 eV = 4.0054 x 10^-18 J

hbar = planck's constant = 1.054 x 10^-34 J.s

then, we get

k = 2 (9.11 x 10^-31 kg) [(4.0054 x 10^-18 J) - (3.2044 x 10^-18 J)] / (1.054 x 10^-34 J.s)²

k = [(1.822 x 10^-30 kg) (8.01 x 10^-19 J)] / (1.110916 x 10^-68 J².s²)

k = 1.313 x 10²⁰ m^-2

k = 1.14 x 10¹⁰ m^-1