2.8 According to classical physics, the average energy of an electron in an electron gas at thermal equilibrium is 3kT/2. Determine, for T = 300 K, the average electron energy (in eV), average electron momentum, and the de Broglie wavelength.

2.8 According to classical physics, the average energy of an electron in an electron gas at thermal equilibrium is 3kT/2. Determine, for T = 300 K, the average electron energy (in eV), average electron momentum, and the de Broglie wavelength.

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter5: Matter Waves

Section: Chapter Questions

Problem 13P

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Question

Question 2.8

gold is 4.90 e V and that
of cesium is 1.90 eV. Calculate the maximum wavelength of light for the photoelectric
emission of electrons for gold and cesium.
(a) The wavelength of green light is A = 550 nm. If an electron has the same wave-
length, determine the electron velocity and momentum. (b) Repeat part (a) for red
light with a wavelength of A = 440 nm. (c) For parts (a) and (b), is the momentum of
the photon equal to the momentum of the electron?
2.6
Determine the de Broglie wavelength for (a) an electron with kinetic energy of
(i) 1.2 eV, (ii) 12 eV, (iii) 120 e V; and for (b) a hydrogen atom with a kinetic energy
2.7
of 1.2 eV.
According to classical physics, the average energy of an electron in an electron gas at
thermal equilibrium is 3kT/2. Determine, for T = 300 K, the average electron energy
(in eV), average electron momentum, and the de Broglie wavelength.
An electron and a photon have the same energy. At what value of energy (in eV) will
the wavelength of the photon be 10 times that of the electron?
2.10 (a) The de Broglie wavelength of an electron is 85 Å. Determine the electron
energy (eV), momentum, and velocity. (b) An electron is moving with a velocity of
8 X 10° cm/s. Determine the electron energy (eV), momentum, and de Broglie wave-
length (in Å).
It is desired to produce x-ray radiation with a wavelength of 1 À. (a) Through what
potential voltage difference must the electron be accelerated in vacuum so that it can,
upon colliding with a target, generate such a photon? (Assume that all of the elec-
tron's energy is transferred to the photon.) (b) What is the de Broglie wavelength of
2.8
2.9
2.11

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