Chapter 39: Q. 6 (page 1136)
FIGURE Q39.6 shows wave packets for particles 1, 2, and 3. Which particle can have its velocity known most precisely? Explain.

Short Answer
The velocity of particle 1 is the most exact.
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Chapter 39: Q. 6 (page 1136)
FIGURE Q39.6 shows wave packets for particles 1, 2, and 3. Which particle can have its velocity known most precisely? Explain.

The velocity of particle 1 is the most exact.
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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?
Suppose you toss three coins into the air and let them fall on the floor. Each coin shows either a head or a tail.
a. Make a table in which you list all the possible outcomes of this experiment. Call the coins A, B, and C.
b. What is the probability of getting two heads and one tail?
c. What is the probability of getting at least two heads?
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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.
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?
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