Learning Materials
Features
Discover
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
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
An electron in an atom can "jump down" from a higher energy level to a lower one, then to a lower one still. The energy the atom thus loses at each jump goes to a photon. Typically, an electron might occupy a level for a nanosecond. What uncertainty in the electron's energy does this imply?
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 )
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?
Because we have found no way to formulate quantum mechanics based on a single real wave function, we have a choice to make. In Section 4.3,it is said that our choice of using complex numbers is a conventional one. Show that the free-particle Schrodinger equation (4.8) is equivalent to two real equations involving two real functions, as follows:
and
where is by definition . How is the complex approach chosen in Section4.3more convenient than the alternative posed here?
A beam of electrons strikes a barrier with two narrow but equal-width slits. A screen is located beyond the barrier. And electrons are detected as they strike the screen. The "center" of the screen is the point equidistant from the slits. When either slit alone is open,electrons arrive per second in a very small region at the center of the screen. When both slits are open, how many electrons will arrive per second in the same region at the center of the screen?
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine