Re: Atom Photon Absorption and Emission Energy

Dear Rich, thank you for our question.  

You asked about the possible differences between the frequencies of light 
absorbed and emitted by metal atoms caused perhaps by “recoil, vibration 
and dissipation as heat.  You mentioned metal atoms and solid metals and 
I think this is where the apparent contradictions in what you have read 
have crept in.

You describe a process of absorption of a photon and it’s re-emission.  
This is a process which can occur with isolated atoms.  When atoms are in 
a gaseous state at very low pressures things are a lot simpler.  In this 
case re-emission takes place before the atom is affected by collisions 
and the emitted photon will usually have the same frequency as the 
absorbed photon.  There are of course, several energy states to which an 
electron can be promoted and if a higher energy state is reached, in 
principle, the electron can drop in energy by stages emitting light of a 
frequency corresponding to the energy drop.  The probability of this will 
depend on the quantum mechanical rules which apply to such transitions.  
( These rules can be transgressed in heavy metals such as mercury whose 
strongest absorption and emission line at 254nm is not strictly allowed 
but “bent” by the effects of spin-orbit coupling ).

At higher pressures an atom which is being excited or is ready to emit a 
photon can be under the influence of adjacent atoms or other gaseous 
components.  In this case, the electron energy levels are less 
predictable and broadening of the absorption and emission lines occurs.  
The exact correspondence between absorbed and emitted light when the 
electron moves between the same two states is then lost and some 
frequency shift can occur in both directions.

When you mention solid metals you mention the electrons ( I’m sure you 
meant electrons not atoms ! ) excited by an absorbed photon jumping 
the “band gap” and you asked if the emission is the same frequency as the 
absorption.  Here we are dealing with a very different situation from a 
gas.  In solids and liquids most electrons promoted in energy by absorbed 
photons lose their energy by conversion to vibrational energy, in other 
words the energy is converted to heat.  Occasionally this process is 
interrupted when a relatively stable excited state is reached and while 
in that state the opportunity to emit a photon can be taken.  This is the 
process of photo-luminescence ( fluorescence between singlet excited 
states or phosphorescence between triplet and singlet states).  The 
emitted photon is therefore normally of lower frequency than the exciting 
photon.  As far as I am aware though, photo-luminescence does not occur 
in solid metals and the absorbed energy finishes up as heat.

Most metals are highly reflective of course but the process of reflection 
is very different from photo-luminescence.  Solid metals are arrays of 
metallic ions which have donated electrons to a population of electrons 
which occupy the “conduction band” of energies.  They are often described 
as the glue keeping the metal ions together and their behaviour has 
parallels with a gas.  They are highly mobile and give metals their 
characteristic high electrical and thermal conductivity.

When a photon impinges on the metal surface the conduction band electrons 
fall under the influence of the oscillating electrical field provided by 
photon.  They are accelerated by this field and since accelerated 
electrons emit electromagnetic radiation, photons are generated.  The 
resulting photons have the same frequency and their directions are 
described by the laws of reflection.  This process then occurs in such a 
way that the reflected light appears to be made up of the self same 
photons which hit the surface and bounced off.

This phenomenon is not confined to metals.  The ions in the ionosphere 
behave in the same way when reflecting radio waves.  Only the dimensions 
are different.