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Jourmal of Tianzhong

Simple Derivation of Kinetic Energy and Quantize Semi axis of Elliptical Orbit in Hydrogen like Atom

Bao Zhang

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

Kinetic energy and quantize semi axis of elliptical orbit of electron in Hydrogen like atom are concisely derived with the help sommerfeld`s quantize condition and based on equation of elliptical orbit.

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European Journal Of Physics Education•Jan 1, 2011•0 citations
Based on the basic coulomb field conservation situation,elliptic equation and quantization rules,a detail derivation process of computation of Sommerfeld's elliptical orbit of stationary state was given.Three equations of physical quantities and ellipse geometry parameters were concisely derived from three conservation situations with the aid of elliptic equation.Making up a new physical quantity,the relationship between the total energy and the equally kinetic of a cycle was given.Using two quantization rules on this base,a derivation on elliptic orbit and energy level of hydrogen-like atom was presented.
The purpose of this work is to present the atomic model proposed by Sommerfeld. We outline the classical calculation of the elliptical orbit and then apply the Wilson–Sommerfeld quantization rules to obtain expressions for the quantization of energy and orbit semi-axes. We then apply the relativistic theory to solve the problem of degenerate orbits. Thus, we see that the Sommerfeld atom is a very rich topic, involving the integration of different subjects ranging from Lagrangian mechanics to relativity, as well as plane geometry and differential equations.