Problems
8.1 What is the probability of drawing a spade from a standard deck of 52 cards?
8.2 What is the probability of drawing a 4 from a standard deck of 52 cards?
8.3 A coin is tossed three times. What is the probability of (a) three heads and (b) two heads
and one tail?
8.4 How many different arrangements of three cards from a standard deck of 52 cards are
possible?
8.5 Four bases (A, C, G, and T) appear in DNA. Assume that the appearance of each base is
random (which is not actually true). What is the probability of observing the following
sequences? (a) AAG; (b) GGG; (c) GGGGAAG; (d) CATCATCATCAT.
8.6 Consider three spins with energies that are ranked with the energy of the up states being
higher than the energy of the down states. For the three spins: (a) how many outcomes
are possible; (b) how many energy states are possible; (c) how does each outcome fit into
the energy ranking?
8.7 Consider two closely lying electronic states that are separated in energy by 9 × 10 −^24 J.
What is the ratio of the number of molecules in the two energy states according to the
Boltzmann distribution at (a) 298K; (b) 4K.
8.8 Consider two closely lying electronic states that are separated in energy by 5 × 10 −^27 J. What
is the ratio of the number of molecules in the two energy states according to the Boltzmann
distribution at (a) 298 K and (b) 4 K?
CHAPTER 8 STATISTICAL THERMODYNAMICS 171
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