Forces and Potential Energy in Atoms

Rutherford s planetary model of the atom assumes that an atom of atomic number Z comprises a dense, central nucleus of positive charge +Ze surrounded by a total of Z electrons moving around the nucleus. The attractive forces between each electron and the nucleus, and the repulsive forces between the electrons, are described by Coulomb s law. We first discuss Coulomb s law in general terms, and then apply it to the planetary atom. 

According to Coulomb s law, the force of interaction between two charges, qi and q2, separated by a distance, r, is 

The potential energy can be calculated from Coulomb s force law, and the result is 

Let s apply these insights to the planetary atom. Associated with each electron (of charge —e) and the nnclens (of charge +Ze) there is potential energy  

the potential energy between the proton and electron separated by 1 A is 

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Chapter 3 before Chapter 6. Those who want to present the full quantum story first and then present the classical description as the limiting case would cover Chapter 3 after Chapter 6. We recommend that both of these sequences cover Section 3.2 (force and potential energy in atoms) before Chapter 4 to give a good physical feeling for Rntherford s planetary model of the atom in preparation for the quantum theory. Instructors who wish to introduce molecular spectroscopy earlier can easily cover Sections 20.1-20.4 immediately after Chapter 6. 

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