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Chapter 39: Q.22 (page 1137)
A thin solid barrier in the plane has a diameter circular hole. An electron traveling in the direction with passes through the hole. Afterward, is it certain that is still zero? If not, within what range is likely to be?
The average velocity is zero. So, the range of velocity is fromto
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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
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?
What is the minimum uncertainty in position, in , of an electron whose velocity is known to be between and ?
Consider a single-slit diffraction experiment using electrons. Using Figure 39.5 as a model, draw
a. A dot picture showing the arrival positions of the first or electrons.
b. A graph of for the electrons on the detection screen.
c. A graph of for the electrons. Keep in mind that , as a wave-like function, oscillates between positive and negative.
3 shows the probability density for an electron that has passed through an experimental apparatus. What is the probability that the electron will land in a 0.010-mm-wide strip at (a) x = 0.000 mm, (b) x = 0.500 mm, (c) x = 1.000 mm, and (d) x = 2.000 mm?
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