Page 248 - Essentials of physical chemistry

210 Essentials of Physical Chemistry

7. The example of the very useful spectrophotometric reagent KMnO 4 is analyzed using ideas
that will be presented in the later chapters of this text to illustrate the concept of electron
orbitals as ‘‘clouds’’ instead of Bohr rings and an illustration is given for an excellent early
calculation of the electronic absorbance of KMnO 4 .

PROBLEMS

9.1 Given the ionization potential of the Li atom is 5.391719 eV, compute the effective nuclear
charge (Z eff ) experienced by the outer 2s electron using the Bohr model. Use the value of Z eff
to calculate the Bohr radius of the 2s orbital.
9.2 Given the ionization potential of the Na atom is 5.139076 eV, compute the effective nuclear
charge (Z eff ) experienced by the outer 3s electron using the Bohr model. Use the value of Z eff
to calculate the Bohr radius of the 3s orbital.
9.3 Given the ionization potential of the K atom is 4.3406633 eV, compute the effective nuclear
charge (Z eff ) experienced by the outer 4s electron using the Bohr model. Use the value of Z eff
to calculate the Bohr radius of the 4s orbital.
9.4 Given the ionization potential of the Rb atom is 4.177128 eV, compute the effective nuclear
charge (Z eff ) experienced by the outer 5s electron using the Bohr model. Use the value of Z eff
to calculate the Bohr radius of the 5s orbital.
9.5 Compute the Bohr radius and the energy of the H atom for n ¼ 1, 2, 3, 4.
9.6 Calculate the energy and radius of the n ¼ 1 orbit for H, He ,Li ,Fe 25þ , and U 91þ .
þ
2þ
9.7 Calculate the energy of the (n ¼ 1) to (n ¼ 2) transition of the H atom in electron volts, wave
numbers, wavelength, and frequency.
9.8 Make a small table of the K a values from Table 9.1, the K a (calc) value and the corrected
* value from the experimental value and the value calculated
value K a(calc) along with the l K a
*
from K a(calc) energy for the following elements: B, Na, Cl, Fe, and Ag.
9.9 Estimate the absorbance (A) of KMnO 4 at 525 nm in curve 2 of Figure 9.5 to calculate the
concentration of the solution.
9.10 Assume that LiF exhibits a first-order Bragg diffraction at an angle of 29.68 for 6.23 keV
x-rays. Use the Bragg’s law to compute the ‘‘d’’ value from this data. Keep in mind that
although LiF has a cubic crystal structure, there are quite a few possible distances that line up
in the crystal when viewed from various angles but what is the ‘‘d’’ for this Bragg reflection?

BIBLIOGRAPHY
Beckhoff, B., B. Kanngieber, N. Langhoff, R. Wedell, and H. Wolff, Handbook of Practical X-Ray
Fluorescence Analysis, Springer, Dorcdrecht, the Netherlands, 2006.
Bertin, E. P., Principles and Practice of X-Ray Spectrometric Analysis, Kluwer Academic=Plenum Publishers.
Buhrke, V. E., R. Jenkins, and D. K. Smith, A Practical Guide for the Preparation of Specimens for XRF and
XRD Analysis, Wiley, New York, 1998.
Jenkins, R., X-Ray Fluorescence Spectrometry, 2nd Edn., Wiley, Chichester, 1999.
Jenkins, R. and J. L. De Vries, Practical X-ray Spectrometry, Springer-Verlag, New York, 1973.
Jenkins, R., R. W. Gould, and D. Gedcke, Quantitative X-Ray Spectrometry, Marcel Dekker, New York, 1981.
Van Grieken, R. E. and A. A. Markowicz, Handbook of X-Ray Spectrometry, 2nd Edn., Vol. 29, Marcel Dekker
Inc, New York, 2002.
X-ray fluorescence, http:==en.wikipedia.org=wiki=X-ray_fluorescence.