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Chapter 4: Q18E (page 134)
A particle is 鈥渢hermal鈥� if it is in equilibrium with its surroundings 鈥� its average kinetic energy would be. Show that the wavelength of a thermal particle is given by
As a result, were able to demonstrate that :
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Experiments effectively equivalent to the electron double slit have been conducted in different, novel ways, producing obvious maxima and minima. Often the point is stressed that the intensity is extremely low. Why is this fact emphasized so much? How low is low enough to make the point?
Determine the momenta that can never be measured when a particle has a wave function.
A beam of electrons strikes a crystal at an anglewith the atomic planes, reflects of many atomic planes below the surface, and then passes into a detector also making anglewith the atomic planes. (a) If the minimumgiving constructive interference is. What is the ratio, Where is the spacing between atomic planes? (b) At what other angles, if any, would constructive interference occur?
The Moon orbits Earth at a radius of . To do so as a classical particle. Its wavelength should be small. But small relative to what? Being a rough measure of the region where it is confined, the orbit radius is certainly a relevant dimension against which to compare the wavelength. Compare the two. Does the Moon indeed orbit as a classical particle? (localid="1659095974931" and )
The proton and electron had been identified by 1920, but the neutron wasn't found until 1932. Meanwhile, the atom was a mystery. Helium, for example, has a mass about four times the proton mass but a charge only twice that of the proton. Of course, we now know that its nucleus is two protons and two neutrons of about the same mass. But before the neutron's discovery, it was suggested that the nucleus contained four protons plus two electrons, accounting for the mass (electrons are "light") and the total charge. Quantum mechanics makes this hypothesis untenable. A confined electron is a standing wave. The fundamental standing wave on a string satisfies , and the "length of the string" in the nucleus is its diameter., so, the electron's wavelength could be no longer than aboutAssuming a typical nuclear radius of determine the kinetic energy of an electron standing wave continued in the nucleus. (Is it moving "slow" or "fast"?) The charge of a typical nucleus is +20e , so the electrostatic potential energy of an electron at its edge would be(it would be slightly lower at the center). To escape. the electron needs enough energy to get far away, where the potential energy is 0. Show that it definitely would escape.
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