Using the Bohr formulas, estimate the average distance from the nucleus for an electron in the innermost (n = 1) orbit in uranium (Z = 92). What is its kinetic energy and potential energy? Approximately how much energy would be required to remove it?

Using the Bohr formulas, estimate the average distance from the nucleus for an electron in the innermost (n = 1) orbit in uranium (Z = 92). What is its kinetic energy and potential energy? Approximately how much energy would be required to remove it?

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter9: Atomic Structure

Section: Chapter Questions

Problem 18P

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The Bohr model

Students often get confused between Rutherford’s model and Bohr model of an atom. They interpret the postulates of both these models to be the same, which is incorrect. Rutherford’s model differs from Bohr’s model in the following ways:

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The energy-level scheme for the hypothetical one electron element Searsium is shown in the figure above. The potential energy is taken to be zero for an electron at an infinite distance from the nucleus. (a) How much energy (in electron volts) does it take to ionize an electron from the ground level? (b) An 18-eV photon is absorbed by a Searsium atom in its ground level. As the atom returns to its ground level, what possible energies can the emitted photons have? Assume that there can be transitions between all pairs of levels. (c) What will happen if a photon with an energy of 8 eV strikes a Searsium atom in its ground level? Why? (d) Photons emitted in the Searsium transitions n = 3 ⟶⟶ n = 2 and n = 3 ⟶⟶ n = 1 will eject photoelectrons from an unknown metal, but the photon emitted from the n = 4 ⟶⟶ n = 3 transition will not. What are the limits (maximum and minimum possible values) of the work function of the metal?