Briefly explain why the magnitude of the absorption coefficient ( \(\beta\) in Equation 21.18) depends on the radiation wavelength.

Absorption coefficient (β) is a parameter used to quantify the absorption of electromagnetic radiation by a medium, such as a gas, liquid, or solid. It represents how much radiation is absorbed by the material per unit length.

When radiation interacts with a material, the energy of the radiation can be absorbed by the material's atoms or molecules if their energy levels match the energy of the radiation. This absorbed energy can cause excitation, ionization, or other changes in the material's state. The absorption coefficient depends on the wavelength because the material's atoms and molecules have different energy levels, which can only absorb radiation with specific energies (or wavelengths) that correspond to the transition between these levels.

The absorption coefficient varies with wavelength because each material has a specific absorption spectrum, i.e., the dependence of absorption on the wavelength. At certain wavelengths, the radiation's energy may align with the allowed energy transitions in the material, leading to high absorption. On the other hand, at other wavelengths, where the radiation's energy does not match any allowed transitions, the material will not absorb much radiation (low absorption coefficient). This variation in the absorption coefficient as a function of wavelength is due to the unique electronic structure of the material and the possible energy transitions it can undergo. ⟩To summarize, the magnitude of the absorption coefficient (β) depends on the radiation wavelength because the absorption of electromagnetic radiation by a material is determined by the interaction between the radiation's energy (wavelength) and the material's atoms or molecules' energy levels. Different materials have unique absorption spectra, which show the varying absorption coefficients at different wavelengths.