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Chapter 39: More About Matter Waves

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Fundamentals Of Physics
Pages: 1186 - 1218
Fundamentals Of Physics

Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

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Illustration

86 Questions for Chapter 39: More About Matter Waves

  1. An electron is trapped in a one-dimensional infinite potential well. For what (a) higher quantum number and (b) lower quantum number is the corresponding energy difference equal to the energy difference ∆E43 between the levels n = 4 and n = 3 ? (c) Show that no pair of adjacent levels has an energy difference equal to 2∆E43 .

    Found on Page 1215

  2. An electron, trapped in a finite potential energy well such as that of Fig. 39-7, is in its state of lowest energy. Are (a) its de-Broglie wavelength, (b) the magnitude of its momentum, and (c) its energy greater than, the same as, or less than they would be if the potential well were infinite, as in Fig. 39-2?

    Found on Page 1214

  3. An electron is trapped in a one-dimensional infinite potential well. For what (a) higher quantum number and (b) lower quantum number is the corresponding energy difference equal to the energy of the n = 5 level? (c) Show that no pair of adjacent levels has an energy difference equal to the energy of the n = 6 level.

    Found on Page 1215

  4. 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.

    Found on Page 1214

  5. An electron is trapped in a one-dimensional infinite well of width250pm and is in its ground state. What are the (a) longest, (b) second longest, and (c) third longest wavelengths of light that can excite the electron from the ground state via a, single photon absorption?

    Found on Page 1215

  6. You want to modify the finite potential well of Fig. 39-7 to allow its trapped electron to exist in more than four quantum states. Could you do so by making the well (a) wider or narrower, (b) deeper or shallower?

    Found on Page 1214

  7. one-dimensional infinite well of length 200 pm contains an electron in its third excited state. We position an electron detector probe of width 2.00 pm so that it is centred on a point of maximum probability density. (a) What is the probability of detection by the probe? (b) If we insert the probe as described 1000 times, how many times should we expect the electron to materialize on the end of the probe (and thus be detected)?

    Found on Page 1215

  8. A hydrogen atom is in the third excited state. To what state (give the quantum number n) should it jump to (a) emit light with the longest possible wavelength, (b) emit light with the shortest possible wavelength, and (c) absorb light with the longest possible wavelength?

    Found on Page 1214

  9. An electron is in a certain energy state in a one-dimensional, infinite potential well from x = 0 to x = L =200PM electron’s probability density is zero at x = 0.300 L , and x = 0.400 L ; it is not zero at intermediate values of x. The electron then jumps to the next lower energy level by emitting light. What is the change in the electron’s energy?

    Found on Page 1215

  10. Figure 39-26 indicates the lowest energy levels (in electronvolts) for five situations in which an electron is trapped in a one-dimensional infinite potential well. In wells B, C, D, and E, the electron is in the ground state. We shall excite the electron in well A to the fourth excited state (at 25 eV). The electron can then de-excite to the ground state by emitting one or more photons, corresponding to one long jump or several short jumps. Which photon emission energies of this de-excitation match a photon absorption energy (from the ground state) of the other four electrons? Give then values.

    Found on Page 1214

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