Research Article

The Rydberg constant and proton size from atomic hydrogen

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Science  06 Oct 2017:
Vol. 358, Issue 6359, pp. 79-85
DOI: 10.1126/science.aah6677

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  • RE: Proton radius related to Bohr radius and fine structure constant (comment by Michael A. Sherbon)
    • Raji Heyrovska, Research Scientist, Academy of Sciences of the Czech rep. (Emeritus)

    Raji Heyrovska replies to Michael Sherbon: The minimum Bohr radius, aH,min given by Eq. 4 in the article is based on reduced mass (see Eq. 2 for Bohr radius). The classical electron radius given by NIST is smaller by the ratio (0.99946) of electron mass to reduced mass, and in fact it corresponds to the limiting case of Eq. 2 when the reduced mass of the atom is almost equal to the electron mass for heavy elements. (See reply to Michael Sherbon by Raji Heyrovska in:

    Competing Interests: None declared.
  • RE: Proton radius related to Bohr radius and fine structure constant

    Noticed that "when the distance between the electron and proton is minimum" of Eq. (4) is also very close to the classical electron radius of 2.81794 fm. More on the golden ratio result and proton radius relation can be found in: Sherbon, M.A. "Quintessential Nature of the Fine-Structure Constant" GJSFR 15, 4: 23-26 (2015).

    Competing Interests: None declared.
  • RE: Proton radius related to Bohr radius and fine structure constant
    • Raji Heyrovska, Research Scientist, Senior Research Scientist (Emeritus), Academy of Sci., Czech Republic

       The radius of the proton has aroused a lot interest since the reported values vary from 0.8335 fm [1] to 0.8751 fm [2]. Here the author shows that the proton radius can be related to the ground state Bohr radius (aH) for hydrogen and the fine structure constant (a) by a simple equation.

       The ground state ionization energy of hydrogen (EH) is related to aH and a by the known relation:

    EH = mHc2a2/2 = e2/8peoaH                                                                            (1)

    where, mH is the reduced mass, c is the speed of light in vacuum, e is the elementary charge, eo is the electric constant. From the values for the constants [2],

    aH = (e2/4peoa2)/mHc2 = 5.294654 x 10-11m  ...

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    Competing Interests: None declared.

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