Learning Materials
Features
Discover
Chapter 4: Q15E (page 134)
How slow would an electron have to be traveling for its wavelength to be at least?
The electron speed is .
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
Determine the momenta that can never be measured when a particle has a wave function.
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.
Electrons are accelerated through a 20 V potential difference producing a monoenergetic beam. This is directed at a double-slit apparatus of 0.010 mm slit separation. A bank of electron detectors is 10 m beyond the double slit. With slit 1 alone open, 100 electrons per second are detected at all detectors. With slit 2 alone open, 900 electrons per second are detected at all detectors. Now both slits are open.
(a) The first minimum in the electron count occurs at detector X. How far is it from the center of the interference pattern?
(b) How many electrons per second will be detected at the center detector?
(c) How many electrons per second will be detected at detector X?
In Example 4.2. neithernorare given units鈥攐nly proportionalities are used. Here we verify that the results are unaffected. The actual values given in the example are particle detection rates, in particles/second, or. For this quantity, let us use the symbol R. It is true that the particle detection rate and the probability density will be proportional, so we may write= bR, where b is the proportionality constant. (b) What must be the units of b? (b) What isat the center detector (interference maximum) in terms of the example鈥檚 given detection rate and b? (c) What would be, and the detection rate R at the center detector with one of the slits blocked?
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?
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