J-However; the efficiency (or electromagnetic frequency) of the accelerating source does, in my opinion, have profound difference on the overall picture. I do not understand how gamma radiation energy is dissipated by the atmosphere. That information I will try to obtain from somewhere.

R.L.- no you clearly don't understand, although MANY here have explained it to you... Here is what happens... The chances that a photon is absorbed depend in many factors, If an atom in the atmosphere is hit by a 1keV photon that happens? It may be absorbed kicking out an inner shell electron. There will be a cascade of transitions emitting photons of lower energies, and there will be a change to the atom and ejected electons KE. The photons emitted scatter off of other atoms as does the original atom and electron....(look up Mean Free Path). Very quickly the original 1keV is distributed among countless atoms and has changed the net temperature by an unmeasureable amount.

Take the same atom and have it 1000 1eV photons- same net result... sure the ionization prcesses will be different but in the end the energy is quickly distributed among uncountable atoms.

J-I will take a candle and light it, then I will put my finger in the flame and keep it there until I can no longer stand the pain, then I will find a source of gamma radiation and will keep my finger in front of it until I can no longer stand the pain. After that I can compare the two fingers and see if there is any difference in the way they have burnt. That experiment should prove to me that the type of energy used to create heat makes no difference as far as the molecules of my body are concerned.

R.L.-The difference is gamma photons break different bonds in your molecules... you release 10 Joules from a candle to burn your finger then you burn your finger and add 10 joules to the earths energy budget. You do that with 10 joules of gamma ray photons many will pass through your finger and get absorbed some where else- some will be absorbed by your finger either way the net energy "added" (it was always there you just chose to release it at that moment...) to the system is 10 Joules.

But please feel free to try your 'experiment'...

You are not only not in the ballpark, you are several A.U. away from it...