\(2\pi.r=f\)
A frequency increases \(r\) decreases. When a photon approaches an orbiting electron, their interaction is electrostatic. The electron is pushed further into the nucleus and like a spring gains energy. When the photon passes, the electron bounces backup. If the stored energy is greater than ionization energy, (ie. the electron's PE at normal orbital radius) the electron is ejected from the atom.
The electron is at light speed around the nucleus. When pushed further into the nucleus, its speed tends to propels it outwards, back to normal orbit. A force exist that oppose the motion of the electron downwards. Such a force is represented by,
\({F}_{s}=\cfrac{{m}_{e}{c^2}}{{r}^2_{e}}\Delta {r}_{e}\)
Let's look at this force further. Like a spring,
\(k=\cfrac{{m}_{e}{c^2}}{{r}^2_{e}}\)
and resonance is at
\({f}_{res}=\cfrac{1}{2\pi}\sqrt{\cfrac{k}{m}}=\cfrac{c}{2\pi{r}_{e}}\), \(m={m}_{e}\)
At this excitation frequency electrons are removed from the atom readily. When electrons are excited by a driving force at this frequency,\({f}_{res}\) with light at the threshold photon frequency, it will resonate. Short pulses at \({f}_{res}\) of light at the metal photoelectric threshold frequency.
A typical value of \({f}_{res}\) is,
For Iron, Fe,
\({f}_{res}\) = 299792458/(2*pi*140e-12) =3.4081e17 Hz, over 340 PHz (peta Hz).
For Gold, Au,
\({f}_{res}\) = 299792458/(2*pi*135e-12) =3.5343e17 Hz, over 353 PHz.
For Copper, Cu,
\({f}_{res}\) = 299792458/(2*pi*135e-12) =3.5343e17 Hz, over 353 PHz.
If this range of oscillation is possible, metal will melt in light.
