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XII.—A Static Model for Helium
Published online by Cambridge University Press: 15 September 2014
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Helium, with atomic number 2, stands second only to hydrogen in interest for the theoretical physicist. The atom would have to consist of a doubly charged positive nucleus and two electrons. “Here,” as Sommerfeld puts it, “we stumble over the three-body problem.” In Bohr's original model of the neutral helium atom the two electrons rotate about the nucleus at opposite ends of a diameter of a circle. The work necessary to detach both electrons, or the second order ionisation potential (if it is expressed in equivalent volts), comes out too great, 82·9 volts instead of 78·6 volts. Later models conceived by Landé and by Bohr clear up some of the difficulties of explaining the separate sets of series described as the parhelium (singlet) and the orthohelium (doublet) series, but according to the calculations of Kramers, the ionisation potential of the crossed orbit model comes out 3·8 volts less than the value experimentally determined. Summing up the present position in his Presidential Address to Section A, at the Liverpool meeting of the British Association, M'Lennan says: “Although real progress has been made, it cannot be said that finality has been reached in the determination of the form of a completely satisfactory model of the atom of so simple an element as helium.”
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References
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page 117 note § It is interesting to observe that the quantum force between nucleus and electron has been assumed equal to e 2an/r 3 and not 2e 2an/r 3, although the nucleus carries a resultant charge of 2e. This assumption, which is necessary to give results in accord with observation, may perhaps be taken to indicate that in the process of “binding” an electron to the nucleus there is a special relation, expressed by the quantum force, between the electron and one of the four “protons” which are supposed to form part of the helium nucleus, for the quantum force is exactly that met with between the “proton” and electron in the case of the hydrogen atom.
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page 119 note † Sommerfeld gives the value 79·3 volts, assuming 25·3 volts as the first ionisation potential. Recent measurements indicate 24·5 volts as a more accurate value for the latter quantity. See Davies, A. C., Phil. Mag., vol. xlv, p. 786, 1923.CrossRefGoogle Scholar)
page 120 note * Bose and Ghosh (Nature, 7th April 1923) have published a photograph of tracks of α particles in helium, in which both the electrons are ejected on the same side of the track of the α particle.
page 123 note * The value obtained from Bohr's original model.
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