Chapter 39: Q 3 Exercise (page 1136)
You are dealt 1 card each from 1000 decks of cards. What is the expected number of picture cards (jacks, queens, and kings)?
Hence the expected number of picture cards is 231.
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A pulse of light is created by the superposition of many waves that span the frequency range , wherc is called thc center frequency of thc pulsc. Lascr technology can generate a pulse of light that has a wavelength of and lasts a mere fs femtosecond localid="1650804865678" .
a. What is the center frequency of this pulse of light?
b. How many cycles, or oscillations, of the light wave are completed during the fs pulse?
c. What range of frequencies must be superimposed to create this pulse?
d. What is the spatial length of the laser pulse as it travels through space?
e. Draw a snapshot graph of this wave packet.
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?
An experiment has four possible outcomes, labeled A to D. The probability of A is PA= 40% and of B is PB = 30%. Outcome C is twice as probable as outcome D. What are the probabilities PCand PD?
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 ?
FIGURE EX39.13 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 -wide strip at (a) , (b), (c) , and (d) ?
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