This electron on passing the kink point on the \(r_e\) vs \(T\) profile will then emit a packet of energy, a fixed quantum, until its oscillation is damped and it can no longer reach the kink point. The size of this quantum of energy is fixed irrespective of the photon energy as long as it is able to provide enough energy that the electron passes beyond the kink on the electron's return.
\(\Delta E_p(f_{th})>E_s(r_{kink},r_{eo})=PE_e(r_{kink})-PE_e(r_{eo})\)
where \(\Delta E_p(f_{th})\) is the energy imparted onto the electron by the photon at frequency \(f_{th}\) as they interact.
For oscillation without immediate ionization, this energy will have to be less than the ionization energy. And photon frequency is related to its radius by,
\(c=2\pi.r_{th} f_{th}\)
where \(r_{th}\) is the radius of the photon circular path at frequency \(f_{th}\).
But if the radius of the photon's helical path is too small, the photon may not be able to push the orbit electron further beyond the kink point. So, we would expect the interaction between the photon and electron to be over a bandwidth of frequencies, for an emission of a quantum (whether the atom is subsequently ionized or not).
\(\Delta E_p(f_{lm})>E_s(r_{kink},r_{eo})=PE_e(r_{kink})-PE_e(r_{eo})\)
Bandwidth,
\(BW=f_{th}-f_{lm}=\cfrac{c}{2\pi}\left\{\cfrac{1}{r_{th}}-\cfrac{1}{r_{lm}}\right\}\)
This energy quantum emitted by the material is perceived as its color! Noted that oscillation is not required for emission of the quantum but repeated emissions requires the electron to oscillate about \(r_{eo}\), its mean orbital radius about the nucleus, passing the kink point each time.
Does a photon then has color? Color of light will be a misnomer.
