Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 29, Problem 4CQ
(a)
To determine
Explain the uncertainty in the radial coordinate of the electron using
(b)
To determine
The uncertainty in the radial component of the velocity of the electron.
(c)
To determine
Does the model violate the uncertainty principle.
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A certain atom has an energy state 3.50 eV above the ground state. When excited to this state, the atom remains for 2.0 ms, on average, before it emits a photon and returns to the ground state. (a) What are the energy and wavelength of the photon? (b) What is the smallest possible uncertainty in energy of the photon?
An electron of a hydrogen atom initially in the third excited state emits a photon and ends up in the ground state. (i) What is the energy in eV and in Joules of the emitted photon? (ii) What is the frequency of the emitted photon?
An electron of momentum p is at a distance r from a stationary proton. The electron has kinetic energy K = p2/2me . The atom has potential energy UE = -kee2/r and total energy E = K + UE. 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 vector momentum is zero, but its average squared momentum is approximately equal to the squared uncertainty in its momentum as given by the uncertainty principle. Treating the atom as a one-dimensional system, (a) estimate the uncertainty in the electron’s momentum in terms of r. Estimate the electron’s (b) kinetic energy and (c) total energy in terms of r. The actual value of r is the one that minimizes the total energy, resulting in a stable atom. Find (d) that value of r and (e) the resulting total energy. (f) State how your answers compare with the predictions of the Bohr theory.
Chapter 29 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 29.2 - Prob. 29.1QQCh. 29.2 - Prob. 29.2QQCh. 29.4 - Prob. 29.3QQCh. 29.5 - Prob. 29.4QQCh. 29.6 - Prob. 29.5QQCh. 29.6 - Prob. 29.6QQCh. 29 - Prob. 1OQCh. 29 - Prob. 2OQCh. 29 - Prob. 3OQCh. 29 - Prob. 4OQ
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