Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Question
Chapter 6, Problem 34P
To determine
Whether the result of problems 32 and 33 are consistent with uncertainty principle.
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Students have asked these similar questions
Problem 2:
An electron of momentum p is at a distancer from a stationary proton. The two particles are interacting
via the electric Coulomb potential. If the electron is bound to the proton to form a hydrogen atom, its
average position is at the proton, but the uncertainty in its position is approximately equal to the radius,
r, of its orbit. The electron's average momentum will be zero, but the uncertainty in its momentum will
be given by the uncertainty principle. Treat the atom as a one-dimensional system to solve the following
questions.
(a) Estimate the uncertainty in the electron's momentum in terms of r.
(b) Estimate the electron's kinetic, potential, and total energies in terms of r.
(c) The actual value of r is the one that minimizes the total energy, resulting in a stable atom. Find that
value of r and the resulting total energy. Compare your answer with the predictions of the Bohr theory.
Consider the half oscillator" in which a particle of mass m is restricted to the region x > 0 by the potential energy
U(x) = 00
for a O
where k is the spring constant.
What are the energies of the ground state and fırst excited state? Explain your reasoning.
Give the energies in terms of the oscillator frequency wo =
Vk/m.
Formulas.pdf (Click here-->)
Let's consider a harmonic oscillator. The total energy of
this oscillator is given by E=(p²/2m) +(½)kx?.
A) For constant energy E, graph the energies in the
range E to E + dE, the allowed region in the classical
phase space (p-x plane) of the oscillator.
B) For k = 6.0 N / m, m = 3.0 kg and the maximum
amplitude of the oscillator xmax =2.3 m For the
region with energies equal to or less than E, the
oscillator number of states that can be entered D(E).
Chapter 6 Solutions
Modern Physics
Ch. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.5 - Prob. 4ECh. 6.7 - Prob. 5ECh. 6.8 - Prob. 6ECh. 6 - Prob. 1QCh. 6 - Prob. 2QCh. 6 - Prob. 3QCh. 6 - Prob. 4QCh. 6 - Prob. 5Q
Ch. 6 - Prob. 6QCh. 6 - Prob. 7QCh. 6 - Prob. 8QCh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10PCh. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 21PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - Prob. 30PCh. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Prob. 33PCh. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - Prob. 37PCh. 6 - Prob. 38P
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