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Chapter 4: Q36E (page 136)
An electron moves along the x-axiswith a well-defined momentum of. Write an expression describing the matter wave associated with this electron. Include numerical values where appropriate.
A statement that describes the matter wave that this electron is linked with
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Question: Atoms in a crystal form atomic planes at many different angles with respect to the surface. The accompanying figure shows the behaviors of representative incident and scattered waves in the Davisson-Germer experiment. A beam of electrons accelerated through 54 V is directed normally at a nickel surface, and strong reflection is detected only at an angle of 500.Using the Bragg law, show that this implies a spacing D of nickel atoms on the surface in agreement with the known value of 0.22 nm.
The uncertainty in the position of a baseball of mass.What is the minimum uncertainty in its speed?
In the hydrogen atom, the electron鈥檚 orbit, not necessarily circular, extends to a distance of a about an angstrom from the proton. If it is to move about as a compact classical particle in the region where it is confined, the electron鈥檚 wavelength had better always be much smaller than an angstrom. Here we investigate how large might be the electron鈥檚 wavelength. If orbiting as a particle, its speed at could be no faster than that for circular orbit at that radius. Why? Find the corresponding wavelength and compare it to . Can the atom be treated classically?
In Exercise 45, the case is made that the position uncertainty for a typical macroscopic object is generally so much smaller than its actual physical dimensions that applying the uncertainty principle would be absurd. Here we gain same idea of how small an object would have鈾� to be before quantum mechanics might rear its head. The density of aluminum is , is typical of solids and liquids around us. Suppose we could narrow down the velocity of an aluminum sphere to within an uncertainty ofper decade. How small would it have to be for its position uncertainty to be at least as large asof its radius?
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 )
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