Physics for Scientists and Engineers with Modern Physics, Technology Update
9th Edition
ISBN: 9781305401969
Author: SERWAY, Raymond A.; Jewett, John W.
Publisher: Cengage Learning
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Question
Chapter 41, Problem 1P
(a)
To determine
The magnitude of de Broglie wavelength.
(b)
To determine
The magnitude of momentum.
(c)
To determine
The kinetic energy in electron volts.
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A free electron has a wave function ψ(x) = Ae i(5.00×1010x)where x is in meters. Find its (a) de Broglie wavelength, (b) momentum, and (c) kinetic energy in electron volts.
A free electron moving along the x-direction (one for which V(x) = 0) would have a wave
function of the form
f(x) = A eikx + B e−ikx
where A and B are constants.
(a) If the wavelength of this wave function (in radians) equals the de Broglie wavelength of
the electron, and its velocity, v = 8.40 × 10² m/sec, what is the value of k (in nm¯¹)?
Express your answer in scientific notation with three significant figures.
(b) The Hamiltonian operator for a free electron is given by
p²
ħ² d²
Ĥ
2me
2me dx²
The wave function provided at the top is an eigenstate of Â. If one measures the energy
for an electron in this state using Â, what would be the result, and how does it compare
to the classical kinetic energy of a free electron with this velocity?
A free electron moving along the x-direction (one for which V(x) = 0) would have a wave
function of the form
f(x) = A eikx + Be -ikx
where A and B are constants.
(a) If the wavelength of this wave function (in radians) equals the de Broglie wavelength of
the electron, and its velocity, v = 8.40 x 10² m/sec, what is the value of k (in nm-¹)?
Express your answer in scientific notation with three significant figures.
(b) The Hamiltonian operator for a free electron is given by
ħ² d²
p²
2me
2m₂ dx²
The wave function provided at the top is an eigenstate of Â. If one measures the energy
for an electron in this state using Â, what would be the result, and how does it compare
to the classical kinetic energy of a free electron with this velocity?
Ĥ =
=
Chapter 41 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
Ch. 41.1 - Prob. 41.1QQCh. 41.2 - Prob. 41.2QQCh. 41.2 - Prob. 41.3QQCh. 41.5 - Prob. 41.4QQCh. 41 - Prob. 1OQCh. 41 - Prob. 2OQCh. 41 - Prob. 3OQCh. 41 - Prob. 4OQCh. 41 - Prob. 5OQCh. 41 - Prob. 6OQ
Ch. 41 - Prob. 7OQCh. 41 - Prob. 8OQCh. 41 - Prob. 9OQCh. 41 - Prob. 10OQCh. 41 - Prob. 1CQCh. 41 - Prob. 2CQCh. 41 - Prob. 3CQCh. 41 - Prob. 4CQCh. 41 - Prob. 5CQCh. 41 - Prob. 6CQCh. 41 - Prob. 7CQCh. 41 - Prob. 8CQCh. 41 - Prob. 1PCh. 41 - Prob. 2PCh. 41 - Prob. 3PCh. 41 - Prob. 4PCh. 41 - Prob. 5PCh. 41 - Prob. 6PCh. 41 - Prob. 7PCh. 41 - Prob. 8PCh. 41 - Prob. 9PCh. 41 - Prob. 10PCh. 41 - Prob. 11PCh. 41 - Prob. 12PCh. 41 - Prob. 13PCh. 41 - Prob. 15PCh. 41 - Prob. 16PCh. 41 - Prob. 17PCh. 41 - Prob. 18PCh. 41 - Prob. 19PCh. 41 - Prob. 20PCh. 41 - Prob. 21PCh. 41 - Prob. 22PCh. 41 - Prob. 23PCh. 41 - Prob. 24PCh. 41 - Prob. 25PCh. 41 - Prob. 26PCh. 41 - Prob. 27PCh. 41 - Prob. 28PCh. 41 - Prob. 29PCh. 41 - Prob. 30PCh. 41 - Prob. 31PCh. 41 - Prob. 32PCh. 41 - Prob. 33PCh. 41 - Prob. 34PCh. 41 - Prob. 36PCh. 41 - Prob. 37PCh. 41 - Prob. 38PCh. 41 - Prob. 39PCh. 41 - Two particles with masses m1 and m2 are joined by...Ch. 41 - Prob. 41PCh. 41 - Prob. 42PCh. 41 - Prob. 43APCh. 41 - Prob. 44APCh. 41 - Prob. 45APCh. 41 - Prob. 46APCh. 41 - Prob. 47APCh. 41 - Prob. 48APCh. 41 - Prob. 49APCh. 41 - Prob. 50APCh. 41 - Prob. 51APCh. 41 - Prob. 52APCh. 41 - Prob. 53APCh. 41 - Prob. 54APCh. 41 - Prob. 56APCh. 41 - Prob. 57APCh. 41 - Prob. 58APCh. 41 - Prob. 59CPCh. 41 - Prob. 60CPCh. 41 - Prob. 61CPCh. 41 - Prob. 62CPCh. 41 - Prob. 63CP
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