Page 47 - Modern physical chemistry

.36 Structure in Molecules and Atoms

2.2 What accelerating voltage is needed to produce an electron beam with a wavelength of
0.100 A?
2.3 Determine the angle sr at which the first minimum and the next maximum occur in formula
(2.31) for i(B).
2.4 An electron beam with wavelength equal to 0.100 A is diffracted by diatomic molecules in
which the interatomic distance is 1.09 A. At what deflection angle B would the first maximum
be observed?
2.5 Construct a Wier! equation for linear S-C-S, letting each scattering factor be proportional
to the corresponding atomic number.
2.6 Calculate the thickness of a lead shield needed to reduce a beam of l4-MeV neutrons to 1.00
per cent of its initial intensity. The cross section for these neutrons is 5.05 barns.
2.7 A target of aluminum 9.00 cm thick absorbed 64.7 per cent of a beam of l4-MeV neutrons.
What cross section is presented by an aluminum atom to the beam?

2.8 The electrons in a beam were accelerated from approximate rest by a potential rise of 30.0
kV. What is the resulting wavelength?
2.9 How is the wavelength of a beam of protons related to the accelerating potential drop V?
2.10 What is the wavelength of a beam of 150 V protons?
2.11 Construct a Wier! equation for benzene, neglecting the contribution of the hydrogen atoms.
2.12 What voltage applied to an X-ray tube will produce photons with wavelengths down to 0.311 A?
2.13 How much is a beam of thermal neutrons reduced on passing through 2.50 cm zinc and 3.50
cm nickel? The pertinent cross section of zinc is 1.06 barns; that of nickel, 4.50 barns.
2.14 An iron shield 2.10 cm thick reduced the intensity of a beam of thermal neutrons by 35.0
per cent. What is the cross section of an iron atom to the beam?

References

Book
Eisberg, R, and Resmick, R: 1974, Quantum Physics oj Atoms, Molecules, Solids, Nuclei, and
Particles, John Wiley & Sons, Inc., New York, pp. 29-134.
This book is essentially an introduction to modem physics. In the part cited, Eisberg and
Resnick introduce the student to simple photon theory, the cross section concept, matter
wave theory, and simple models of the atom.
Articles
Dantus, M., Kim, S. B., Williamson, J. C., and Zewail, A H.: 1994, "Ultrafast Electron Diffraction.
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Hanson, R Fl., and Bergman, S. A: 1994, "Data-Driven Chemistry: Building Models of Molecular
Structure (Literally) from Electron Diffraction Data," J. Chem. Educ. 71, 150-152.
Heilbronner, E.: 1989, "Why do Some Molecules Have Symmetry Different from that Expected?"
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Heyrovska, R: 1992, "On Neutron Numbers and Atomic Masses," J. Chem. Educ. 69, 742-743.
Kidd, R, Ardini, J., and Anton, A: 1988, "Evolution of the Modem Photon," Am. J. Phys. 57, 27-35.
King, R B.: 1996, "The Shapes of Coordination Polyhedra," J. Chem. Educ. 73,993-997.
Nelson, P. G.: 1997, "Valency," J. Chem. Educ. 74, 465- 470.
Pullen, B. P.: 1986, "Cerenkov Counting of 4°K in KC1 Using a Liquid Scintillation Spectrometer,"
J. Chem. Educ. 63, 971.
Sacks, L. J.: 1986, "Coulombic Models in Chemical Bonding," J. Chem. Educ. 63, 288-296.
Weinrach, J. B., Carter, K. L., Bennett, D. W, and McDowell, H. K.: 1990, "Point Charge Approxi-
mations to a Spherical Charge Distribution," J. Chem. Educ. 67, 995-999.
Williamson, J. C., and Zewail, A H.: 1994, "Ultrafast Electron Diffraction. 4. Molecular Structures
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