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Chapter 39: Q 8 Exercise (page 1136)
1.0x 1010 photons pass through an experimental apparatus. How many of them land in a 0.10-mm-wide strip where the probability density is 20 m-1?
Thus, the number of photons that will land in 0.10 mm wide strip is
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Consider the electron wave function
where x is in nm. a. Determine the normalization constant c.
b. Draw a graph of c1x2 over the interval -5 nm 鈥� x 鈥� 5 nm. Provide numerical scales on both axes.
c. Draw a graph of 0 c1x2 0 2 over the interval -5 nm 鈥� x 鈥� 5 nm. Provide numerical scales.
d. If 106 electrons are detected, how many will be in the interval -1.0 nm 鈥� x 鈥� 1.0 nm?
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 ?
Consider the electron wave function
where x is in nm.
a. Determine the normalization constant c.
b. Draw a graph of over the interval role="math" localid="1650907186096" .
Provide numerical scales on both axes.
c. Draw a graph of over the interval role="math" localid="1650907657944" .
Provide numerical scales.
d. If electrons are detected, how many will be in the interval
role="math" localid="1650908765290" ?
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 small speck of dust with mass has fallen into the hole shown in FIGURE P39.46 and appears to be at rest. According to the uncertainty principle, could this particle have enough energy to get out of the hole? If not, what is the deepest hole of this width from which it would have a good chance to escape?
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