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Chapter 39: Q11Q (page 1214)
From a visual inspection of Fig. 39-8, rank the quantum numbers of the three quantum states according to the de Broglie wavelength of the electron, greatest first.
According to de Broglie wavelength, the electron rank of the quantum states with gratest first is n = 1, n = 2, n = 3.
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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?
An electron is trapped in a finite potential well that is deep enough to allow the electron to exist in a state with n = 4. How many points of (a) zero probability and (b) maximum probability does its matter wave have within the well?
Calculate the probability that the electron in the hydrogen atom, in its ground state, will be found between spherical shells whose radii are a and 2a , where a is the Bohr radius?
Let be the energy difference between two adjacent energy levels for an electron trapped in a one-dimensional infinite potential well. Let E be the energy of either of the two levels. (a) Show that the ratio approaches the value at large values of the quantum number n. As , does (b) (c) E or, (d) approaches zero? (e) what do these results mean in terms of the correspondence principle?
Figure 39-30 shows a two-dimensional, infinite-potential well lying in an xy plane that contains an electron. We probe for the electron along a line that bisects and find three points at which the detection probability is maximum. Those points are separated by 2.00 nm . Then we probe along a line that bisects and find five points at which the detection probability is maximum. Those points are separated by 3.00 nm . What is the energy of the electron?
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