\(\sqrt[3]{N}.2\pi a_{\psi\,c}=\lambda_\beta\)
and
\(\cfrac{ave.\,E\alpha}{E\beta}=\sqrt[3]{\cfrac{N+1}{N}}\)
\(\cfrac{N+1}{N}=\left(\cfrac{ave.\,E\alpha}{E\beta}\right)^3\)
\(\cfrac{N+1}{N}=(\cfrac{1.54184}{1.39222})^3=1.36\)
\(N=9\)
since,
\(\cfrac{9+1}{9}=1.37\)
So,
\(a_{\psi\,c}=\cfrac{\lambda_\beta}{\sqrt[3]{N}.2\pi }\)
\(a_{\psi\,c}=\cfrac{1.39222}{\sqrt[3]{9}.2\pi }\)
\(a_{\psi\,c}=0.10493e-10=0.010493\,\,nm\)
This is the first time we have actually obtained \(a_{\psi\,\,c}\) from experimental data. It is however, way smaller than expected, because,
\(\sqrt[3]{N}.a_{\psi\,c}=a_{\psi\,\small{N}}\)
when \(N=77\)
\(a_{\psi\,\small{N}}=4.4639e-11\,\,m\)
which smaller than the values for \(a_{\psi}\) obtained from hydrogen spectra lines experiments, in the post "Sizing Them Up" dated 3 Dec 2014.
Nonetheless,
\(f_{res}=0.061\cfrac { c }{ a_{\psi} }\)
\(f_{res}=0.061\cfrac { 299792458 }{ \sqrt[3]{9}*0.10493e-10 }\)
\(f_{res}=0.83786*10^{18}\,\,Hz\)
which is nine times less than the previously calculated value of \(f_{res}=7.473*10^{18} Hz\). And so the current that would cause resonance is,
\(I_{res}=\cfrac{1.1974}{9}=0.13304\,\,A\)
This current reduced by an integer divisor will also cause resonance but slower. Currents higher by an integer multiplier than \(I_{res}\) will not caused resonance. But it is,
\(\sqrt[3]{N}.a_{\psi\,c}=\sqrt[3]{9}*0.10493e-10=2.1826e-11\)
that is resonating. What is this entity than is about nine times bigger than the previous value,
\(a_{\psi}=0.2447e-11\)
Does,
\(\sqrt[3]{N}.2\pi a_{\psi\,c}=\lambda_\beta\)
make sense in the first place? Or,
\(N.2\pi a_{\psi}=\lambda_\beta\)
What is happening here? What are we setting into resonance? \(a_{\psi\,c}\), \(\sqrt[3]{N}a_{\psi\,c}\) or \(Na_{\psi}\)?
The lower values for \(a_{\psi\,c}\) suggests that,
\(\cfrac{a_{\psi\,1}}{a_{\psi\,1}}=\left(\cfrac{N_1}{N_2}\right)^3\)
maybe wrong; that when particles merge, the total volume of \(\psi\) may not be conserved.
The expression, \(N.a_{\psi}\) suggests that,
If \(a_{\psi}\) being stack up is true, then it would be impossible to obtain X ray from atomized \(Cu\) vapor nor non-homogeneous alloys of \(Cu\) where \(a_{\psi}\) cannot stack up.
