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Chapter 39: Q. 28 (page 1118)
FIGURE P39.28 shows a pulse train. The period of the pulse train is , where is the duration of each pulse. What is the maximum pulse-transmission rate (pulses per second) through an electronics system with a bandwidth? (This is the bandwidth allotted to each FM radio station.)
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In an interference experiment with electrons, you find the most intense fringe is at x = 7.0 cm. There are slightly weaker fringes at x= 6.0 and 8.0 cm, still weaker fringes at x = 4.0 and 10.0 cm, and two very weak fringes at x= 1.0 and 13.0 cm. No electrons are detected at x <0 cm or x> 14 cm.
a. Sketch a graph of is for these electrons.
b. Sketch a possible graph of .
c. Are there other possible graph for? If so draw one
FIGURE P39.32 shows for the electrons in an experiment.
a. Is the electron wave function normalized? Explain.
b. Draw a graph of over this same interval. Provide a numerical scale on both axes. (There may be more than one acceptable answer.)
c. What is the probability that an electron will be detected in a -wide region at? At ? At
d. If electrons are detected, how many are expected to land in the interval ?
When 5 X 1012 photons pass through an experimental apparatus, 2.0 X 109 land in a 0.10-mm-wide strip. What is the probability density at this point?
Soot particles, from incomplete combustion in diesel engines, are typically in diameter and have a density of . FIGURE P39.45 shows soot particles released from rest, in vacuum, just above a thin plate with a -diameter holeroughly the wavelength of visible light. After passing through the hole, the particles fall distance d and land on a detector. If soot particles were purely classical, they would fall straight down and, ideally, all land in a -diameter circle. Allowing for some experimental imperfections, any quantum effects would be noticeable if the circle diameter were . How far would the particles have to fall to fill a circle of this diameter?
A -mm-diameter sphere bounces back and forth between two walls at and . The collisions are perfectly elastic, and the sphere repeats this motion over and over with no loss of speed. At a random instant of time, what is the probability that the center of the sphere is
a. At exactly ?
b. Between and ?
c. At ?
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