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Inverse Square Square Model for Bohr

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Inverse Biquadrate Model for Bohr is one of atom model to acommodate inverse square saquare gravity which is also electric force.

Force equation is given as follows

F = G_3 Mm/r^4 = mr \omega^2

Energy equation is given as follows

E = mv^2 /2 - G_3 Mm/(3r^3 )

Quantization contition for Bohr was given for angular momentum.

L = nh/2 \pi

Above condition is no good for inverse biquadrate gravity. Alternatively, the condition that T is proportional to nnn seems fitting.

But we would like to fit energy level for backward compatability.

r = r_0 n^{4/3}


E_{nk} = 1/3 ( G_3 Mm/ 2 r_0 ^3 ) (1/n^2 +1/k^2 ) (1/n^2 -1/k^2 )

Bohr modelEdit

The combination of natural constants in the energy formula is called the Rydberg energy (RE):

 R_E = { (k_e e^2)^2 m_e \over 2 \hbar^2}

This expression is clarified by interpreting it in combinations which form more natural units:

\, m_e c^2 is the rest mass energy of the electron (511 keV/c)
\, {k_e e^2 \over \hbar c} = \alpha \approx {1\over 137} is the fine structure constant
\, R_E = {1\over 2} (m_e c^2) \alpha^2

Since this derivation is with the assumption that the nucleus is orbited by one electron, we can generalize this result by letting the nucleus have a charge q = Ze where Z is the atomic number. This will now give us energy levels for hydrogenic atoms, which can serve as a rough order-of-magnitude approximation of the actual energy levels. So, for nuclei with Z protons, the energy levels are (to a rough approximation):

 E_n = -{Z^2 R_E \over n^2}


note that total enery is positive and inside electron has high energy. and, with newly enhanced g",

Failed to parse (lexing error): GEFR =G"/G_{3} =0.8455  %

Radial wave functionEdit

Radial wave function for inverse biquadrate force diverges. Probably, Radial wave function is delta function.

see alsoEdit

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