Learning Materials
Features
Discover
Chapter 4: Q22E (page 135)
Roughly speaking for what range of wavelengths would we need to treat an electron relativistically, and what would be the corresponding range of accelerating potentials? Explain your assumptions.
Rane of Wavelength and Range of Accelerating potentials:
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
What is the density of a solid'? Although the mass densities of solids vary greatly, the number densities (in ) vary surprisingly little. The value. of course, hinges on the separation between the atoms-but where does a theoretical prediction start? The electron in hydrogen must not as a particle orbiting at a strict radius, as in the Bohr atom. but as a diffuse orbiting wave. Given a diffuse probability, identically repeated experiments dedicated to "finding" the electron would obtain a range of values - with a mean and standard deviation (uncertainty). Nevertheless, the allowed radii predicted by the Bohr model are very close to the true mean values.
(a) Assuming that atoms are packed into a solid typically jBohr radii apart, what would be the number of moles per cubic meter?
(b) Compare this with the typical mole density in a solid of. What would be the value of j?
Question: Analyzing crystal diffraction is intimately tied to the various different geometries in which the atoms can be arranged in three dimensions and upon their differing effectiveness in reflecting waves. To grasp some of the considerations without too much trouble, consider the simple square arrangement of identical atoms shown in the figure. In diagram (a), waves are incident at angle with the crystal face and are detected at the same angle with the atomic plane. In diagram (b), the crystal has been rotated 450 counterclockwise, and waves are now incident upon planes comprising different sets of atoms. If in the orientation of diagram (b), constructive interference is noted only at an angle, at what angle(s) will constructive interference be found in the orientation of diagram (a)? (Note: The spacing between atoms is the same in each diagram.)
The energy of a particle of massbound by an unusual spring is.
(a) Classically. it can have zero energy. Quantum mechanically, however, though both andare "on average" zero, its energy cannot be zero. Why?
(b) Roughly speaking.is a typical value of the particle's position. Making a reasonable assumption about a typical value of its momentum, find the particle's minimum possible energy.
A beam of particles, each of mass m and (nonrelativistic) speed v, strikes a barrier in which there are two narrow slits and beyond which is a bunk of detectors. With slit 1 alone open, 100 particles are detected per second at all detectors. Now slit 2 is also opened. An interference pattern is noted in which the first minimum. 36 particles per second. Occurs at an angle of 30ofrom the initial direction of motion of the beam.
(a) How far apart are the slits?
(b) How many particles would be detected ( at all detectors) per second with slit 2 alone open?
(c) There are multiple answers to part (b). For each, how many particles would be detected at the center detector with both slits open?
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?
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App