How does carbon dioxide in the atmosphere keep heat trapped?

Question

In the classic description of how greenhouses gases are increasing the temperature of Earth's surface, shorter wavelengths of light like visible and ultraviolet (UV) penetrate the atmosphere, hit the ground, and come back as infrared light that cannot pass through the carbon dioxide in the atmosphere. According to my research, $\ce{CO2}$ absorbs wavelengths around $15 \,\pu{\mu m}$ or infrared best. When molecules absorb energy, it does so by bumping electrons to higher energy levels.

I have the following questions now:

1. Why can $\ce{CO2}$ not absorb arbitrarily high amounts of energy?

2. Why is the wavelength of light when it hits earth different than what is spit out when an electron goes back to ground?

Answer 1

$\ce{CO2}$, like all other matter, can only absorb photons of energies corresponding to some kind of quantum transition with a high transition probability, whether that is a rotational, vibrational, electronic, or nuclear transition. These possible transitions are not continuously distributed over all energies. Within the IR region of light, only a few vibrational transitions of $\ce{CO2}$ can absorb light with high probability.

The light released from the earth's surface, just like the sun's surface, is blackbody radiation. The blackbody radiation spectrum is temperature dependent. Higher temperatures allow for release of more photons of higher energy. The sun is much hotter than earth so it releases more visible blackbody radiation while the low-temperatures of Earth's surface gives a peak in the blackbody radiation spectrum squarely in the IR.

Answer 2

Your first question. A CO2 molecule can absorb many quanta one after the other provided the wavelength is correct and there are sufficient number of photons /second. This can happen if you excite with a v powerful ir. laser. Normally, in the atmosphere, the number of photons is so small that the CO2 has radiated the extra energy away or lost it in a collision.

Second question. If the wavelength striking the earth is in the visible this causes an electronic transition in any molecule absorbing it, say chlorophyll in a plant. This energy is used to make biomass but the process is not 100% efficient so some energy is lost and this becomes heat in the surroundings. In rocks and soil, electronic transitions also occur but now the excited state decays by transferring energy to the surroundings in non-radiative (i.e. 'dark') transitions to the ground state and again heating nearby molecules.

Third question. The CO2 does not of itself keep the heat trapped in the atmosphere but clearly is involved in doing so. The CO2 absorbs ir radiation emitted from warm molecules on the earth's surface, warmed by the processes described above. After absorption a warmed CO2 can radiate into space or back the the ground again and this process can be repeated many times so most photons would eventually get radiated away if nothing else happens. However, most of the atmosphere is O2 and N2 (CO2 is at $\approx 0.04$% so tiny) and as a result any CO2 suffers numerous collisions/second which can remove any excess vibrational/rotational energy present as a result of absorbing ir radiation. The O2/N2 are now hotter than the were but cannot radiate away this energy (as CO2 can) because they have no dipole, and so by colliding with other similar molecules spread the energy and the atmosphere warms.