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 28, Problem 20CQ
To determine
Elaborate the point that electron behaves sometimes like a particle and sometimes like a wave.
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When we model light (EM radiation) as a particle, we
call it a photon a packet of energy. How does this
work with the model of light as a wave? To think
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If the intensity of a beam of light is related to the
number of photons passing per second, how would
you explain the intensity of light using the model of
light as a wave? What feature (wavelength, frequency,
amplitude, oscillation, etc.) can be a measure of
intensity and why do you think so?
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The treatment of electrons in atoms must be a quantum treatment, but classical physics still works for baseballs. Where is the dividing line? Suppose we consider a spherical virus, with a diameter of 30 nm, constrained to exist in a long, narrow cell of length 1.0 μm. If we treat the virus as a particle in a box, what is the lowest energy level? Is a quantum treatment necessary for the motion of the virus?
Let's think more about de Broglie's relation.
Macro scale matters have wave nature, i.e., wavelength?
(1) Our (humans) movements also have wavelength?
Calculate wavelength of a human with a speed of 1 m/s.
(2) How about electrons whose mass is extremely light?
Calculate wavelength of an electron with a speed of 1 m/s.
Chapter 28 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 28.1 - Prob. 28.1QQCh. 28.2 - Prob. 28.2QQCh. 28.2 - Prob. 28.3QQCh. 28.2 - Prob. 28.4QQCh. 28.5 - Prob. 28.5QQCh. 28.5 - Prob. 28.6QQCh. 28.6 - Prob. 28.7QQCh. 28.10 - Prob. 28.8QQCh. 28.10 - Prob. 28.9QQCh. 28.13 - Prob. 28.10QQ
Ch. 28 - Prob. 1OQCh. 28 - Prob. 2OQCh. 28 - Prob. 3OQCh. 28 - Prob. 4OQCh. 28 - Prob. 5OQCh. 28 - Prob. 6OQCh. 28 - Prob. 7OQCh. 28 - Prob. 8OQCh. 28 - Prob. 9OQCh. 28 - Prob. 10OQCh. 28 - Prob. 11OQCh. 28 - Prob. 12OQCh. 28 - Prob. 13OQCh. 28 - Prob. 14OQCh. 28 - Prob. 15OQCh. 28 - Prob. 16OQCh. 28 - Prob. 17OQCh. 28 - Prob. 18OQCh. 28 - Prob. 1CQCh. 28 - Prob. 2CQCh. 28 - Prob. 3CQCh. 28 - Prob. 4CQCh. 28 - Prob. 5CQCh. 28 - Prob. 6CQCh. 28 - Prob. 7CQCh. 28 - Prob. 8CQCh. 28 - Prob. 9CQCh. 28 - Prob. 10CQCh. 28 - Prob. 11CQCh. 28 - Prob. 12CQCh. 28 - Prob. 13CQCh. 28 - Prob. 14CQCh. 28 - Prob. 15CQCh. 28 - Prob. 16CQCh. 28 - Prob. 17CQCh. 28 - Prob. 18CQCh. 28 - Prob. 19CQCh. 28 - Prob. 20CQCh. 28 - Prob. 1PCh. 28 - Prob. 2PCh. 28 - Prob. 3PCh. 28 - Prob. 4PCh. 28 - Prob. 6PCh. 28 - Prob. 7PCh. 28 - Prob. 8PCh. 28 - Prob. 9PCh. 28 - Prob. 10PCh. 28 - Prob. 11PCh. 28 - Prob. 13PCh. 28 - Prob. 14PCh. 28 - Prob. 15PCh. 28 - Prob. 16PCh. 28 - Prob. 17PCh. 28 - Prob. 18PCh. 28 - Prob. 19PCh. 28 - Prob. 20PCh. 28 - Prob. 21PCh. 28 - Prob. 22PCh. 28 - Prob. 23PCh. 28 - Prob. 24PCh. 28 - Prob. 25PCh. 28 - Prob. 26PCh. 28 - Prob. 27PCh. 28 - Prob. 29PCh. 28 - Prob. 30PCh. 28 - Prob. 31PCh. 28 - Prob. 32PCh. 28 - Prob. 33PCh. 28 - Prob. 34PCh. 28 - Prob. 35PCh. 28 - Prob. 36PCh. 28 - Prob. 37PCh. 28 - Prob. 38PCh. 28 - Prob. 39PCh. 28 - Prob. 40PCh. 28 - Prob. 41PCh. 28 - Prob. 42PCh. 28 - Prob. 43PCh. 28 - Prob. 44PCh. 28 - Prob. 45PCh. 28 - Prob. 46PCh. 28 - Prob. 47PCh. 28 - Prob. 48PCh. 28 - Prob. 49PCh. 28 - Prob. 50PCh. 28 - Prob. 51PCh. 28 - Prob. 52PCh. 28 - Prob. 53PCh. 28 - Prob. 54PCh. 28 - Prob. 55PCh. 28 - Prob. 56PCh. 28 - Prob. 57PCh. 28 - Prob. 58PCh. 28 - Prob. 59PCh. 28 - Prob. 60PCh. 28 - Prob. 61PCh. 28 - Prob. 62PCh. 28 - Prob. 63PCh. 28 - Prob. 64PCh. 28 - Prob. 65PCh. 28 - Prob. 66PCh. 28 - Prob. 67PCh. 28 - Prob. 68PCh. 28 - Prob. 69PCh. 28 - Prob. 70PCh. 28 - Prob. 71PCh. 28 - Prob. 72PCh. 28 - Prob. 73PCh. 28 - Prob. 74P
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- When you solve Schrodinger equation for your system you'll finally get well defined energy levels with no uncertainty related to them. Isn't it a contradiction to universal uncertainty principle? How do you explain this ( use appropriate equations)?arrow_forwardAt time t = 0 the wave function for a particle in a box is given by the function in the provided image, where ψ1(x) and ψ1(x) are the ground-state and first-excited-state wave functions with corresponding energies E1 and E2, respectively. What is ψ(x, t)? What is the probability that a measurement of the energy yields the value E1? What is <E>?arrow_forwardQuestion 1: It is not possible to observe the effect of De Broglie wave particle duality and Heisenberg uncertainty principle in daily life. But these two phenomenon are observable in case of subatomic particles like electron. Prove this observation with the help of suitable examples and discussion.arrow_forward
- A single electron of mass m can move freely along a one-dimensionl gold nanowire. Let x be the position coordinate of the electron along the wire. (a) Let ø (x) be the wave function of the electron. The quantity |ø (x)| has dimensions of inverse length. Explain very briefly the meaning of this quantity as a probability density. (b) Let us assume that $ (x) = A sin (3kox) (2) where A and ko are fixed, positive constants. Establish whether this wave function represents an eigenstate of momentum p. Justify your answer. Hint: the momentum operator is p -ih. - (c) Establish whether the wave function (x) given in Eq. (2) represents an eigenstate of kinetic energy K. Justify your answer. Hint: the kinetic energy operator is K = p²/2m. (d) Let us now assume that the gold nanowire mentioned above is not infinite, but extends over a finite length from r= 0 to x = L. Inside this region, the potential energy of the electron is zero, but outside this region the potential energy is infinite…arrow_forwardWhich of the following statements related to quantum statistics are true? Select one or more: a.The wave function of a pair of bosons is symmetric with respect to the exchange of particles. b.If the particle density of an ideal gas is very low (that is, the particle density is much less than the cube of the thermal de Broglie wavelength), quantum effects are important. c.In the case of a rare gas and at high enough temperatures, the Fermi-Dirac and Bose-Einstein distributions are approximately the same. d.Two bosons cannot be in the same quantum state.arrow_forwardTrue or false? Classical mechanics is based on the principle of uncertainty and predicts all phenomena in terms of probabilities. It describes a sub-atomic world which is totally different from the world at macroscopic scales.arrow_forward
- Do you think it is reasonable to describe the Schrodinger equation as a postulate of quantum mechanics? What is a postulate?arrow_forwardWhen an electron and a proton of the same kinetic energy encounter a barrier of the same height and width, which one of them will tunnel through the barrier more easily? Why?arrow_forwardYou are interested in investigating the atomic structure of a sample with a beam of electrons. The atomic structure has a characteristic size of 0.100 nm. Knowing that the observable detail of the atomic struture is limited to about the wavelength of the probe (electrons, in this case), to what speed should you accelerate the electrons in the beam? You may assume the electrons speed is non relativistic. Hint: de Brogile matter waves!arrow_forward
- What is the smallest box in which you can confine an electron if you want to know for certain that the uncertainty in the electron’s speed is no more than 20 m/s?arrow_forwardFor a particle in a box, what would the probability distribution function Ic I2 look like if the particle behaved like a classical (Newtonian) particle? Do the actual probability distributions approach this classical form when n is very large? Explain.arrow_forwarda. Conceptually, discuss the particle-wave duality of light. Discuss the implications of this in combination with the de Broglie (pronounced “de Broy”) equation. b. The electron of a hydrogen atom is usually no further than 1.0 Å from the proton. We can therefore say the upper limit of the radius of an isolated hydrogen atom is roughly 1.0 Å. How does the de Broglie wavelength of the electron compare to this radius? (The velocity of an electron in the first principal energy level is about 2.2 x 106 m/s). Explain why wave-particle duality is so important for quantum mechanics, yet not required in macroscopic systems that are well described by classical mechanics. c. Comment as to whether neutrons with velocity 4.14 x 103 m/s may be used to determine structures of molecules in a diffraction-based experiment. You may consider the relevant distance between atoms in molecules to be on the order of 1 Å.arrow_forward
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