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Chapter 28

Problem 1

What is the de Broglie wavelength of a basketball of mass \(0.50 \mathrm{kg}\) when it is moving at \(10 \mathrm{m} / \mathrm{s} ?\) Why don't we see diffraction effects when a basketball passes through the circular aperture of the hoop?

Problem 4

What is the magnitude of the momentum of an electron with a de Broglie wavelength of \(0.40 \mathrm{nm} ?\)

Problem 6

The distance between atoms in a crystal of \(\mathrm{NaCl}\) is $0.28 \mathrm{nm} .$ The crystal is being studied in a neutron diffraction experiment. At what speed must the neutrons be moving so that their de Broglie wavelength is \(0.28 \mathrm{nm} ?\)

Problem 8

What are the de Broglie wavelengths of electrons with the following values of kinetic energy? (a) \(1.0 \mathrm{eV}\) (b) $1.0 \mathrm{keV} .

Problem 11

A nickel crystal is used as a diffraction grating for x-rays. Then the same crystal is used to diffract electrons. If the two diffraction patterns are identical, and the energy of each \(\mathrm{x}\) -ray photon is \(E=20.0 \mathrm{keV},\) what is the kinetic energy of each electron?

Problem 20

A hydrogen atom has a radius of about \(0.05 \mathrm{nm}\) (a) Estimate the uncertainty in any component of the momentum of an electron confined to a region of this size. (b) From your answer to (a), estimate the electron's kinetic energy. (c) Does the estimate have the correct order of magnitude? (The ground-state kinetic energy predicted by the Bohr model is \(13.6 \mathrm{eV} .\) )

Problem 26

Nuclei have energy levels just as atoms do. An excited nucleus can make a transition to a lower energy level by emitting a gamma-ray photon. The lifetime of a typical nuclear excited state is about 1 ps. What is the uncertainty in the energy of the gamma-rays emitted by a typical nuclear excited state? [Hint: Use the energy-time uncertainty principle, Eq. \((28-3) .]\)

Problem 27

What is the minimum kinetic energy of an electron confined to a region the size of an atomic nucleus \((1.0 \mathrm{fm}) ?\)

Problem 35

What is the ground state electron configuration of a \(\mathrm{K}^{+}\) ion?

Problem 37

What are the possible values of \(L_{z}\) (the component of angular momentum along the \(z\) -axis) for the electron in the second excited state \((n=3)\) of the hydrogen atom?

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