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Chapter 39: Q57P (page 1217)
An electron is trapped in a one-dimensional infinite potential well. Show that the energy difference between its quantum levels n and n+2 is .
It is proved that .
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Consider a conduction electron in a cubical crystal of a conducting material. Such an electron is free to move throughout the volume of the crystal but cannot escape to the outside. It is trapped in a three-dimensional infinite well. The electron can move in three dimensions so that its total energy is given by
in whichare positive integer values. Calculate the energies of the lowest five distinct states for a conduction electron moving in a cubical crystal of edge length .
Figure 39-29 a shows a thin tube in which a finite potential trap has been set up where . An electron is shown travelling rightward toward the trap, in a region with a voltage of , where it has a kinetic energy of 2.00 eV. When the electron enters the trap region, it can become trapped if it gets rid of enough energy by emitting a photon. The energy levels of the electron within the trap are , and , and the non quantized region begins at as shown in the energylevel diagram of Fig. 39-29b. What is the smallest energy such a photon can have?
Three electrons are trapped in three different one-dimensional infinite potential wells of widths (a) 50pm (b)200pm, and (c)100pm . Rank the electrons according to their ground-state energies, greatest first.
A diatomic gas molecule consists of two atoms of massseparated by a fixed distance drotating about an axis as indicated in given figure. Assuming that its angular momentum is quantized as in the Bohr model for the hydrogen atom, find
An electron is trapped in a one-dimensional infinite potential well that is 100 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width centered at x = (a) 25 pm, (b) 50 pm, and (c) 90 pm? (Hint: The interval x is so narrow that you can take the probability density to be constant within it.)
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