Chapter 39: Q. 21 (page 1137)
What minimum bandwidth is needed to transmit a pulse that consists of 100 cycles of a oscillation?
The minimum bandwidth is needed to transmit a pulse that consists of 100 cycles of a oscillation is .
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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
In one experiment, 2000 photons are detected in a 0.10-mm- wide strip where the amplitude of the electromagnetic wave is 10 V/m. How many photons are detected in a nearby 0.10-mm- wide strip where the amplitude is 30 V/m?
Consider a single-slit diffraction experiment using electrons. (Single-slit diffraction was described in Section 33.4.) Using Figure 39.5 as a model, draw
a. A dot picture showing the arrival positions of the first 40 or 50 electrons.
b. A graph of for the electrons on the detection screen.
c. A graph of for the electrons. Keep in mind that , as a wave-like function, oscillates between positive and negative.
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?
Physicists use laser beams to create an atom trap in which atoms are confined within a spherical region of space with a diameter of about . The scientists have been able to cool the atoms in an atom trap to a temperature of approximately , which is extremely close to absolute zero, but it would be interesting to know if this temperature is close to any limit set by quantum physics. We can explore this issue with a onedimensional model of a sodium atom in a -long box.
a. Estimate the smallest range of speeds you might find for a sodium atom in this box.
b. Even if we do our best to bring a group of sodium atoms to rest, individual atoms will have speeds within the range you found in part a. Because there's a distribution of speeds, suppose we estimate that the root-mean-square speed of the atoms in the trap is half the value you found in part a. Use this to estimate the temperature of the atoms when they've been cooled to the limit set by the uncertainty principle.
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