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Chapter 40: Q. 12 (page 1175)
A helium atom is in a finite potential well. The atom鈥檚 energy isbelow . What is the atom鈥檚 penetration distance into the classically forbidden region?
The penetration depth is
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The correspondence principle says that the average behavior of a quantum system should begin to look like the Newtonian solution in the limit that the quantum number becomes very large. What is meant by 鈥渢he average behavior鈥� of a quantum system?
An electron approaches a wide potential-energy barrier of height . What energy electron has a tunneling probability of (a) 10%, (b) 1.0%, and (c) 0.10%?
Four quantum particles, each with energy E, approach the potential-energy barriers seen in FIGURE Q40.8 from the left. Rank in order, from largest to smallest, the tunneling probabilities
Tennis balls traveling faster than routinely bounce off tennis rackets. At some sufficiently high speed, however, the ball will break through the strings and keep going. The racket is a potential-energy barrier whose height is the energy of the slowest string-breaking ball. Suppose that atennis ball traveling at is just sufficient to break the -thick strings. Estimate the probability that a ball will tunnel through the strings without breaking them. Give your answer as a power of rather than a power of.
a. What is the probability that an electron will tunnel through aair gap from a metal to a STM probe if the work function is ?
b. The probe passes over an atom that is鈥渢all.鈥� By what factor does the tunneling current increase?
c. If a current change is reliably detectable, what is the smallest height change the STM can detect?
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