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.
Given: Graphs for wave functions of each particle.
When compared to particle 1, the wave functions of particles 2 and 3 are less spatially stretched. The more specific the position is known, the less precise the momentum is known, according to Heisenberg's Uncertainty Principle. Particles 2 and 3 have more exact position because their wave functions are less spatially stretched, but they have less precise momentum.
The most exact momentum belongs to particle 1.
A small speck of dust with mass has fallen into the hole shown in FIGURE P39.46 and appears to be at rest. According to the uncertainty principle, could this particle have enough energy to get out of the hole? If not, what is the deepest hole of this width from which it would have a good chance to escape?
An electron that is confined to x Ú 0 nm has the normalized wave function c1x2 = b 0 x 6 0 nm 11.414 nm-1/2 2e-x/11.0 nm2 x Ú 0 nm where x is in nm. a. What is the probability of finding the electron in a 0.010-nmwide region at x = 1.0 nm? b. What is the probability of finding the electron in the interval 0.50 nm … x … 1.50 nm?
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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