transition between in particular molecules. The relationship between the energy change of a given molecule[1] and an electromagnetic wave with wavelength λ is:

 ${\displaystyle \Delta E=\hbar /\lambda }$ (4h)

where ${\displaystyle \hbar }$ is the reduced Planck constant (${\displaystyle h/2\pi }$), so larger energy transitions correspond to shorter wavelengths. When ${\displaystyle \Delta E}$ is positive, a photon is absorbed by the molecule; when ${\displaystyle \Delta E}$ is negative, a photon is emitted by the molecule. Possible transitions are limited by open energy levels of the atoms composing a given atom, so in general triatomic molecules (e.g. water, with its two hydrogen and single oxygen atoms) are capable of interesting interactions with a larger spectrum of wavelengths than are diatomic molecules (e.g. carbon monoxide, with its single carbon and single oxygen atoms), since the presence of three atomic nuclei generally means more open energy orbital states.[2]

Because the incoming solar radiation and the outgoing radiation leaving the Earth are of very different wavelengths, they interact with the gasses in the atmosphere very differently. Most saliently, the atmosphere is nearly transparent with respect to the peak wavelengths of incoming radiation, and nearly opaque (with some exceptions) with respect to the peak wavelengths of outgoing radiation. In the figure below, the E/M spectrum is represented on the x-axis, and the absorption efficiency (i.e. the probability that a molecule of the gas will absorb a photon when it encounters an E/M wave of the given wavelength) of various molecules in Earth’s atmosphere is represented on the y-axis. The peak emission range of incoming solar radiation is colored

1. All of what follows here holds for simple atoms as well, though free atoms are relatively rare in the Earth’s atmosphere, so the discussion will be phrased in terms of molecules.
2. For details, see Mitchell (1989)

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