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Chapter 4: Q26E (page 135)
A beam of electrons of kinetic energy is directed at a single slip of 2.0 μm width, then detected at a screen 4m beyond the slit. How far from a point directly in the line of the beam is the first location where no electrons are ever detected?
The line of the beam is detected at
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The p0 is a subatomic particle of fleeting existence. Data tables don't usually quote its lifetime. Rather, they quote a "width," meaning energy uncertainty, of about 150MeV. Roughly what is its lifetime?
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.)
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?
In Example 4.2. neithernorare given units—only 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’s given detection rate and b? (c) What would be, and the detection rate R at the center detector with one of the slits blocked?
Question: When we refer to a “bound” particle, we usually mean one for which there is no probability of finding it outside some finite confines. Could a bound particle be perfectly dead stationary, meaning a well-defined velocity of zero? Why or why not?
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