\(f(n)=\left(\cfrac{\sqrt[3]{n}-{1}}{\sqrt[3]{n}}\right)\)
| n | f(n) |
|---|---|
| 70 | 0.7573572497 |
| 71 | 0.758501808 |
| 72 | 0.7596250716 |
| 73 | 0.7607277244 |
| 74 | 0.7618104192 |
| 75 | 0.7628737797 |
| 76 | 0.7639184021 |
| 77 | 0.7649448568 |
| 78 | 0.7659536896 |
| 79 | 0.7669454232 |
The value of \(f(n)\) for the range \(70\le n\le79\) average to
\(f(n)=0.762\)
from which we may estimate \(f_{\psi\,c}\) from,
\(\Delta E_{2\rightarrow 1}=h.f_{\psi\,c}\left(\cfrac{\sqrt[3]{n_2}-\sqrt[3]{n_1}}{\sqrt[3]{n_1}\sqrt[3]{n_2}}\right)\)
where \(n_1=1\)
from the post "Sizing Them Up Again..." dated 4 Oct 2016.
But what is \(n\) or \(n_{\small{large}}\)?
Better yet since the emission spectra line as the result of \((n_2=2,\,n_1=1)\), (two basic particles, \(n=1\) coalesce) that produces a pair of photons, \(\Delta E_{1\rightarrow 2}\) has double the intensity and hence readily identifiable,
\(\Delta E_{1\rightarrow 2}=h.f_{\psi\,c}\left(\cfrac{\sqrt[3]{2}-\sqrt[3]{1}}{\sqrt[3]{1}\sqrt[3]{2}}\right)\)
where \(n_1=1\) and \(n_2=2\).
\(\Delta E_{1\rightarrow 2}=h.f_{\psi\,c}\left(\cfrac{\sqrt[3]{2}-1}{\sqrt[3]{2}}\right)\)
\(\Delta E_{1\rightarrow 2}=0.2063hf_{\psi\,c}\)
without worry about what \(n_{\small{large}}\) might be.
This is different from Planck's relation \(E=h.f\). A factor of about \(\frac{1}{5}\) creeps in.
