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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
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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

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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