Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-17T05:28:46.813Z Has data issue: false hasContentIssue false
  • English
  • Français

The total energy of binding of a heavy atom

Published online by Cambridge University Press:  24 October 2008

E. A. Milne
E. A. Milne
Affiliation:
Trinity College
Get access Rights & Permissions [Opens in a new window]

Abstract

Thomas's differential equation for the average field inside a heavy atom is analogous to Emden's equation for the polytropic equilibrium of a star. Emden's result that the total gravitational potential energy of a star is calculable once the differential equation has been solved is adapted to give the total electrostatic energy, and hence the total energy of binding, of an atom built on Thomas's model. This should be equal to the sum of the successive ionisation potentials. The total energy is found to be proportional to N, where N is the atomic number. The values found agree with Hartree's calculations of the successive ionisation potentials of certain atoms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 23 , Issue 7 , July 1927 , pp. 794 - 799
Copyright
Copyright © Cambridge Philosophical Society 1927

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

* “The calculation of atomic fields,” Proc. Camb. Phil. Soc., 23, 1927, 542.CrossRefGoogle Scholar

† Emden, , Gaskugeln, Leipzig, 1907.Google Scholar

‡ This adaptation ia due to Eddington.Google Scholar

* We have replaced Thomas's ρ throughout by ξ, to avoid confusion with our use ρ for charge-density.Google Scholar

* Corrected value, kindly supplied by Mr Thomas.Google Scholar

† Proc. Camb. Phil. Soc., 22, 473, 1924.Google Scholar