Quantum Physics

Problems 9335. Is it possible for a spectrum from an x-ray tube toshow the continuous spectrum of x-rays without thepresence of the characteristic x-rays?6. Suppose that the electron in the hydrogen atomobeyed classical mechanics rather than quantummechanics. Why should such a hypothetical atomemit a continuous spectrum rather than the observedline spectrum?7. When a hologram is produced, the system (includinglight source, object, beam splitter, and so on)must be held motionless within a quarter of thelight’s wavelength. Why?8. If matter has a wave nature, why is it not observablein our daily experience?9. Discuss some consequences of the exclusion principle.10. Can the electron in the ground state of hydrogenabsorb a photon of energy less than 13.6 eV? Can itabsorb a photon of energy greater than 13.6 eV?Explain.11. Why do lithium, potassium, and sodium exhibit similarchemical properties?12. List some ways in which quantum mechanics alteredour view of the atom pictured by the Bohr theory.13. It is easy to understand how two electrons (one withspin up, one with spin down) can fill the 1s shell for ahelium atom. How is it possible that eight more electronscan fit into the 2s, 2p level to complete the1s2s 2 2p 6 shell for a neon atom?14. The ionization energies for Li, Na, K, Rb, and Csare 5.390, 5.138, 4.339, 4.176, and 3.893 eV, respectively.Explain why these values are to be expectedin terms of the atomic structures.15. Why is stimulated emission so important in the operationof a laser?16. The Bohr theory of the hydrogen atom is basedupon several assumptions. Discuss these assumptionsand their significance. Do any of them contradictclassical physics?17. Explain why, in the Bohr model, the total energy ofthe hydrogen atom is negative.18. Consider the quantum numbers n, , m , and m s .(a) Which of these are integers and which are fractional?(b) Which are always positive and which canbe negative? (c) If n 2, what is the largest value of? (d) If 1, what are the possible values of m ?19. Photon A is emitted when an electron in a hydrogenatom drops from the n 3 level to the n 2 level.Photon B is emitted when an electron in a hydrogenatom drops from the n 4 level to the n 2 level.(a) In which case is the wavelength of the emittedphoton greater? (b) In which case is the energy ofthe emitted photon greater?PROBLEMS1, 2, 3 = straightforward, intermediate, challenging = full solution available in Student Solutions Manual/Study Guide= coached problem with hints available at www.cp7e.com = biomedical applicationSection 28.1 Early Models of the AtomSection 28.2 Atomic Spectra1. Use Equation 28.1 to calculate the wavelengthof the first three lines in the Balmer series for hydrogen.2. Show that the wavelengths for the Balmer series satisfythe equation 364.5n2n 2 4 nmwhere n 3, 4, 5, . . .3. The “size” of the atom in Rutherford’s model isabout 1.0 10 10 m. (a) Determine the attractiveelectrostatic force between an electron and a protonseparated by this distance. (b) Determine (in eV)the electrostatic potential energy of the atom.4. The “size” of the nucleus in Rutherford’s model ofthe atom is about 1.0 fm 1.0 10 15 m. (a) Determinethe repulsive electrostatic force betweentwo protons separated by this distance. (b) Determine(in MeV) the electrostatic potential energyof the pair of protons.5.The “size” of the atom in Rutherford’smodel is about 1.0 10 10 m. (a) Determinethe speed of an electron moving about the protonusing the attractive electrostatic force between anelectron and a proton separated by this distance.(b) Does this speed suggest that Einsteinian relativitymust be considered in studying the atom?(c) Compute the de Broglie wavelength of the electronas it moves about the proton. (d) Does thiswavelength suggest that wave effects, such as diffractionand interference, must be considered in studyingthe atom?