Modern Physics for Scientists and Engineers
Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 4, Problem 55P
To determine

Show that the quantization of angular momentum L=nh follows Bohr’s assumption D that the mean value K  of the kinetic energy of the electron nucleus system is given by K=nhforb2 .

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A sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, the Bohr model does not apply, because the neutral atom contains 11 electrons instead of a single electron. However, we can apply the model to the outermost electron as an approximation, provided that we use an effective value Zeffective rather than 11 for the number of protons in the nucleus. (a) The ionization energy for the outermost electron in a sodium atom is 5.1 eV. Use the Bohr model with Z = Zeffective to calculate a value for Zeffective. (b) Using Z = 11, determine the corresponding value for the radius r of the outermost Bohr orbit. (c) Using the value calculated for Zeffective in part (a), determine the corresponding radius r of the outermost Bohr orbit. (a) Zeffective = Number i 2.04 (b) _r= (c)_r= Number i 5.29E-11 Number i 2.12E-11 Units No units Units m Units m ♥
Show that the quantization of angular momentum L= nh follows from Bohr’s Assumption D that the mean value K of the kinetic energy of the electronnucleus system is given by K = nhforb/2. Assume a circular orbit.
In a one electron system, the probability of finding the electron within a shell of thickness år at a radius of r from the nucleus is given by the radial distribution function, P(r) = ?R? (r). An electron in a 1s hydrogen orbital has the radial wavefunction R (r) given by 3/2 R(r) = 2 ela where a, is the Bohr radius (52.9 pm). Calculate the probability of finding the electron in a sphere of radius 0.80ao centered at the nucleus. 10.99 probability: Incorrect
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