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Trigonometric derivations of the fine structure constant, the proton charge radius, the proton to electron mass ratio, the electron charge to mass ratio and the classical expressions for the Compton wavelengths

Volume 5, Issue 6, December 2020    |    PP. 118-134    |PDF (1026 K)|    Pub. Date: December 8, 2020
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Author(s)
Emmanuel Saucedo-Flores, DIP-CUCEI Universidad de Guadalajara, José Guadalupe Zuno No. 48, 45101 Zapopan, Jalisco, México

Abstract
Over 20 physical definitions of the Sommerfeld or fine-structure constant α are derived using sine functions plots of a few H atom-related parameters; the presence of the particle-wave duality in most of the derived expressions is indicated. Five expressions for the electron charge to mass ratio are also established. An approximation for the arithmetic value of the proton charge radius is proposed. Also, several analytical expressions for the proton to electron mass ratio are provided. An expression using proton parameters to calculate the exact 2018 CODATA recommended value of Planck constant h is obtained. hc, h/c, h/qP/c and Compton wavelengths equations having the quantum = classical configuration were established.

Keywords
Fine-structure constant, proton charge radius, proton to electron mass ratio, electron charge to mass ratio, geometrical mean of a0 and re

Cite this paper
Emmanuel Saucedo-Flores, Trigonometric derivations of the fine structure constant, the proton charge radius, the proton to electron mass ratio, the electron charge to mass ratio and the classical expressions for the Compton wavelengths, SCIREA Journal of Physics. Vol. 5 , No. 6 , 2020 , pp. 118 - 134 .

References

[ 1 ] Kragh, H., “Magic Number: A Partial History of the Fine-Structure Constant” Arch. Hist. Exact Sci. 57, 395–431 (2003). https://doi.org/10.1007/s00407-002-0065-7
[ 2 ] Mohr, P. J.; Taylor, B. N.; Newell, D. B., (2019), "Fine structure constant". CODATA Internationally recommended 2018 values of the fundamental physical constants. National Institute of Standards and Technology. All NIST values shown in manuscript were last retrieved on 15 October 2020
[ 3 ] Backerra, Anna C. M. “Relation between Planck’s Constant and Speed of Light, Predicting Proton Radius More Accurately “Applied Physics Research; Vol. 11, No. 5; 2019 ISSN 1916-9639 E-ISSN 1916-9647 Published by Canadian Center of Science and Education doi:10.5539/apr.v11n5p1
[ 4 ] Saucedo-Flores, Emmanuel, “The proton charge radius and the proton to electron mass ratio equations” SCIREA Journal of Physics Volume 5, Issue 5, October 2020, PP. 108-117, PDF (231 K) , Pub. Date: October 11, 2020