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 - V_{0}) / (hbar)^{2}

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

V_{0} = 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} J^{2}.s^{2})

k = _{
}1.313 x 10^{20} m^{-2}

**k = 1.14 x 10 ^{10} m^{-1}**

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