Re-emission of Absorbed Radiation
When a molecule of carbon dioxide absorbs radiation, it re-emits the radiation in femto seconds. The time can be calculated based on wavelength of the radiation. Each wave of emitted radiation is a vibration back and forth by the molecule emitting it.
All matter emits radiation in this manner—the amount based on the temperature as indicated by the Stefan-Boltzmann constant. Radiation emitted this way by all matter is called black body radiation.
As molecules vibrate, they impart some kinetic energy to the molecules which they strike, and they emit some energy as radiation. The exact ratio varies with conditions and is too complex to determine exactly, but it can be guessed at for a rough estimate.
This image shows how energy is re-distributed when radiation is absorbed by carbon dioxide.
This is a one-time absorption of radiation.
When a molecule of CO2 in the atmosphere absorbs fingerprint radiation (the only thing in question) it increases in vibratory motion, which is heat. As it bumps into surrounding molecules (mostly nitrogen gas), it imparts some motion, which reduces its own motion, while increasing the motion of the other molecule. This bumping goes from molecule to molecule, as the energy spreads through the atmosphere.
The vibrating motion of molecules sends out waves of infrared radiation. As the molecular motion decreases, the intensity of the radiation and its frequency get lower.
The amount of such bumping and re-emitting that must occur to lose the energy gained by absorption depends upon how strong the radiation is that is absorbed, which is determined by the temperature of the emitting molecules. Emissions from the surface of the earth into the atmosphere would go from warmer to colder. For short distances in the atmosphere, the emitting temperature would be about the same as the absorbing temperature.
Absorbed radiation (fingerprint radiation) is weaker than emitted radiation (black body radiation), because 8% of black body radiation is fingerprint radiation for these conditions.
The average wavelength of radiation emitted by CO2 at near-surface temperatures would be around 25 microns, which is about the center of the graph above. In emitting radiation at 25 microns, there are 83 femto seconds for each initial bump. (frequency equals velocity over wavelength. Time equals inverse of frequency) (3x108 ÷ 25x10-6 = 12x1012, inverse = 83x10-15).
When temperatures are equal for emission and absorption, radiation absorbed by carbon dioxide would be re-emitted within the time required for five wavelengths or bump cycles. Five times 83 femto seconds is 415 femto seconds, or about half of a pico second.
Why five cycles? CO2 absorbs finger print radiation in three peaks, the strongest one at 15 microns of wavelength. It then emits the energy as black body radiation due to the vibration of the molecules. Weak radiation is absorbed and stronger radiation is emitted, except that kinetic energy (heat, when averaged) is also being imparted to nearby molecules at the same time. Those molecules also emit radiation. By the time five bumps occur, the initial radiation energy would be re-emitted.
Continuous Energy Transfer
The one-time analysis is a close representation of a continuous analysis. An analysis of continuous absorption and re-emision of radiation goes like this: Each time a CO2 molecule bumps a surrounding molecule, it loses half its energy through conduction, and it loses energy through radiation. But the energy is constantly being replaced. Losing half of the energy while being replaced at the same rate would result in three fourths of the energy being retained.
Since each CO2 molecule in the atmosphere is surrounded by 2,500 air molecules, it would have to be 2,500°C to heat the surrounding molecules to an average temperature of 1°C. But transferring energy to surrounding molecules while absorbing radiation would slightly lower the hypothetically required temperature of 2,500°C. Reduction to three fourths would be 1875°C.
The CO2 molecule is also emitting radiation while absorbing radiation. If rates were equal, another reduction by half would be required for loss of energy to sustain the needed temperature, which results in 2188°C being the required temperature for transferring enough heat to the surrounding 2,500 air molecules for 1°C average air temperature increase. The remaining 312 units of heat as temperature increase would be distributed between the molecules which CO2 bumps into. It would bump into about five surrounding molecules heating each one by 62°Cthat is to get the required 1°C total over 2,500 molecules.
However, the absorbed radiation is fingerprint radiation, which is weaker than the emitted radiation, which is black body radiation. The fingerprint radiation which CO2 absorbs is 8% of black body radiation. This means emission is 12.5 times stronger than absorption.
But equilibrium would require emission to equal absorption. The higher tendency to emit than to absorb would drag down the temperature increase by CO2. Hypotheticals break down at this point, because the needed 2,500°C is a total absurdity to start with.
These extremely high temperatures are absurd. They are what would be required to get a 1°C average increase in the atmosphere. In actuality, the CO2 molecules cannot be much different in temperature than surrounding molecules, which is why the whole concept of greenhouse gases is absurd.
What would actually occur is that the CO2 would only be heated trillionths of a degree centigrade, and no greenhouse effect would occur. Why trillionths of a degree? Because radiation is extremely weak. It's energy is dissipated in femto seconds. The energy cannot build up. This effect rides on top of normal temperatures, which are mostly produced through conduction, convection and evaporation.
If energy were coming from a warm earth and going into a cold atmosphere, more time would be required to re-emit the energy. But most of the radiation in the atmosphere moves less than ten meters, because saturation occurs within ten meters