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Volume 15: Pages 439-443, 2002
On the Equation H = mv2 and the Fine Structure of the Hydrogen Atom
Ezzat G. Bakhoum
New Jersey Institute of Technology, P.O. Box 305, Marlton, New Jersey 08053 U.S.A.
The recent [Phys. Essays 15, 1 (2002)] reconciliation of the theories of special relativity and wave mechanics implies that the mass‐energy equivalence principle must be expressed mathematically as H = mv2, where H is the total energy of a particle, m is its relativistic mass, and v is its velocity, not as H = mc2, as was widely believed. In this paper the equation H = mv2 will be used to calculate the energy levels in the spectrum of the hydrogen atom. It is demonstrated that the well‐known Sommerfeld‐Dirac formula is still obtained, but without the constant term m0c2 that was originally present in the formula.
Keywords: mass‐energy equivalence, atomic spectra, hydrogen spectrum, finestructure constant, Sommerfeld‐Dirac formula
Received: August 20, 2002; Published online: December 15, 2008