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Chapter 39: Q 9 Exercise (page 1136)
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?
Thus, the probability density is
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a. Starting with the expressionfor a wave packet, find an expression for the product
for a photon.
b. Interpret your expression. What does it tell you?
c. The Bohr model of atomic quantization says that an atom in an excited state can jump to a lower-energy state by emitting a photon. The Bohr model says nothing about how long this process takes. You'll learn in Chapter 41 that the time any particular atom spends in the excited state before emitting a photon is unpredictable, but the average lifetime of many atoms can be determined. You can think of as being the uncertainty in your knowledge of how long the atom spends in the excited state. A typical value is . Consider an atom that emits a photon with a wavelength as it jumps down from an excited state. What is the uncertainty in the energy of the photon? Give your answer in .
d. What is the fractional uncertainty in the photon's energy?
FIGURE Q39.1 shows the probability density for photons to be detected on the-axis.
a. Is a photon more likely to be detected at or at ? Explain.
b. One million photons are detected. What is the expected number of photons in a -wide interval at ?
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?
FIGURE P39.46
What is the smallest one-dimensional box in which you can confine an electron if you want to know for certain that the electron’s speed is no more than 10 m/s?
What minimum bandwidth is needed to transmit a pulse that consists of 100 cycles of a oscillation?
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