Chapter 39: Q.18 (page 1137)
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So the length of the pulse will be
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a. Starting with the expression for 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 cmitting a photon is unprcdictablc, 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 ns. 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 eV.
d. What is the fractional uncertainty in the photon's energy?
Andrea, whose mass is , thinks she’s sitting at rest in her long dorm room as she does her physics homework. Can Andrea be sure she’s at rest? If not, within what range is her velocity likely to be?
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 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?
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?
Heavy nuclei often undergo alpha decay in which they emit an alpha particle (i.e., a helium nucleus). Alpha particles are so tightly bound together that it's reasonable to think of an alpha particle as a single unit within the nucleus from which it is emitted.
a. nucleus, which decays by alpha emission, is in diameter. Model an alpha particle within nucleus as being in a onc-dimensional box. What is the maximum specd an alpha particle is likely to have?
b. The probability that a nucleus will undergo alpha decay is proportional to the frequency with which the alpha particle reflects from the walls of the nucleus. What is that frequency (reflections/s) for a maximum-speed alpha particle within a nucleus?
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