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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 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?
|You learned in Chapter 37 that, except for hydrogen, the mass of a nucleus with atomic number Z is larger than the mass of the Z protons. The additional mass was ultimately discovered to be due to neutrons, but prior to the discovery of the neutron it was suggested that a nucleus with mass number A might contain A protons and (A-Z) electrons. Such a nucleus would have the mase of A protone, but ite net charge would be only Z o.
a. We know that the diameter of a nuclens is approximately 10 fmm. Model the nucleus as a one-dimensional box and find the minimum range of speeds that an electron would have in such a box.
b. What does your answer imply about the possibility that the nucleus contains electrons? Explain.
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.
The probability density of finding a particle somewhere along thethe probability density is . For, the probability density decreases by a factor of each time the distance from the origin is doubled. What is the probability that the particle will be found in the interval
The probability density for finding a particle at position is
and zero elsewhere
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