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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?
The probability density for an electron that has passed through an experimental apparatus. If electrons are used, what is the expected number that will land in alocalid="1649312933417" wide strip atlocalid="1649312941736" and localid="1649312949893" ?
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 15fm in diameter. Model an alpha particle within a nucleus as being in a one-dimensional box. What is the maximum speed 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?
The probability density for finding a particle at position is
and zero elsewhere
Ultrasound pulses with a frequency of are transmitted into water, where the speed of sound is . The spatial length of each pulse is localid="1650889451408" localid="1650889457691" .
a. How many complete cycles are contained in one pulse?
b. What range of frequencies must be superimposed to create each pulse?
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