Radiation escaping from the atmosphere equilibrates with radiation entering from the sun in about 100 pico seconds.

Most radiation which cools the planet leaves from the atmosphere, and very little from the surface of the earth. The Kiehl-Trenberth model says 79% of the energy leaving the surface of the earth is in the form of radiation with 21% attributed to conduction and evaporation. Since this amount of radiation is extremely ridiculous, the NASA energy budget reduced the radiation to 41% with 59% leaving through conduction and evaporation. But still, only white hot metals would emit 41% radiation in an air environment. In actuality, radiation would be 1-3% of the energy leaving the surface of the earth.

Recently, NASA reverted to the Kiehl-Trenberth model saying 79% of the energy leaving the earth's surface is in the form of radiation. Apparently, the NASA lab tried to make the number look less ridiculous by reducing it somewhat, but they could not remove the poured-in-concrete number of 79%, so they reverted back to it to eliminate inconsistency.

About 30% of the radiation entering the atmosphere from the surface of the earth goes around greenhouse gases. Wikipedia says 15-30%. It would be closer to 30%, because bandwidths for greenhouse gases separate significantly in the atmosphere. For the rough calculations here, we will use 20% as the amount of infrared, back body radiation going around greenhouse gases and into space to cool the planet.

As a CO2 molecule absorbs radiation, it vibrates more rapidly, which is an increase in heat. While vibrating, it is giving up its gained energy, some as radiation and some as heat conducted into the air molecules which it bumps. No one can say how much energy goes either way or how long it takes. We can roughly estimate that half of the energy would go each way in 100 vibrations.

As explained on the temperature page, an average wavelength for emissions would be something like 25 microns, which means 83 femto seconds per vibration. For calculations, let's say each vibration gives up 1% of the gained energy as radiation, and 1% as heat. After the first vibration, 20% of the radiation emitted goes into space to cool the planet. That's 20% of the 1% of the gained energy by the CO2 molecule. The CO2 molecule then has 98% of its gained energy.

With the second vibration, 20% of the next 1% cools the planet. That's 0.2% of the energy with each vibration. After 100 vibrations, its 20%. After 200 vibrations, it's 40%. Theses numbers are averages and proportionalities over varying conditions.

Notice that even though only 20% of the radiation goes into space to cool the planet, it is a repeated 20% which very rapidly adds up. It is 40% in 17 pico seconds. It is 20% each time radiation is emitted, while it is being emitted repeatedly.

Even though this analysis deals with one wave, which cannot be split into pieces, the average of the total radiation includes the variations.

Each of the air molecules which are heated also emit their energy as radiation in a similar manner. Even though 80% of the energy does not go into space, it keeps being radiate until it does, and it only takes pico seconds for equilibrium to be re-estaablished at the temperature which balances inflow with outflow.

This means radiation cools the atmosphere very rapidly until it emits the same amount of radiation into space as enters. Blocking radiation is nonsense. Absorption of radiation causes re-emission of the radiation into space in pico seconds.