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Chapter 39: Q 4 Exercise (page 1136)
Suppose you draw a card from a regular deck of 52 cards.
a. What is the probability that you draw an ace?
b. What is the probability that you draw a spade?
Hence, the probability of getting an ace is
and the probability of getting spades is
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FIGURE P39.31 shows the wave function of a particle confined
between x = 0 nm and x = 1.0 nm. The wave function is zero
outside this region.
a. Determine the value of the constant c, as defined in the figure.
b. Draw a graph of the probability density
c. Draw a dot picture showing where the first 40 or 50 particles
might be found.
d. Calculate the probability of finding the particle in the interval
.
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?
A particle is described by the wave function c1x2 = b cex/L x … 0 mm ce-x/L x Ú 0 mm where L = 2.0 mm.
a. Sketch graphs of both the wave function and the probability density as functions of x.
b. Determine the normalization constant c.
c. Calculate the probability of finding the particle within 1.0 mm of the origin. d. Interpret your answer to part b by shading the region representing this probability on the appropriate graph in part a
You are dealt 1 card each from 1000 decks of cards. What is the expected number of picture cards (jacks, queens, and kings)?
A 1.0-mm-diameter sphere bounces back and forth between two walls at and . The collisions are perfectly elastic, and the sphere repeats this motion over and over with no loss of speed. At a random instant of time, what is the probability that the center of the sphere is
a. At exactly ?
b. Between and ?
c. At ?
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