Fandom

Gravity Wiki

Inverse Square Square Model for Bohr

771pages on
this wiki
Add New Page
Talk0 Share

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}

then,


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}

GEFREdit

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

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.