Maxwell's equations describe the interaction electric and magnetic fields both in space as they interact with matter. One solution of the equations gives a wave equation, which corresponds to propagating electromagnetic radiation. Like any wave, electromagnetic radiation has a wavelength and a frequency. However, the speed of electromagnetic radiation is a constant in vacuum.
Although Maxwell's equations appear to be a complete and self-consistent theory there are observations in the natural world that are not explained by Maxwell's theory. One aspect is the consequence of the fixed speed of light. That aspct gives rise to the theory of relativity, which is mentioned here only to illustrate the point that Maxwell's theory is not complete. The second aspect is thermal radiation, which implies that light is quantized. How do we reconcile the quantizaton of light with the wave nature of light? This answer is the definition of the wave-particle duality..
The wave theory explains macroscopic phenomena such as reflection, refraction, and diffraction, but it also exaplains the interaction of light with molecules in the sense that the wave nature of light reveals that light has an angular momentum. We can see this in the fact that the electromagnetic wave has a node. The node is the line of zero intensity, which is pointed along the direction of travel. We call the vector along the direction of propagation, the Poynting vector. The node of the wave is important for our understanding of absorption since the node carries angular momentum. We shall shortly justify the use of quantum numbers, but for now we will assume that the number of nodes on the radiation or on an atom is equal to the angular momentum quantum number. This is shown below.
The sheer size of the wave is a problem if we consider the absorption of light by atoms and molecules. A typical molecule might be 1 or 2 nm in size. Visible light has wavelengths between 400-700 nm. Thus, the wavelenght of light is at least 200 times larger than a typical molecule. There is no easy way to picture how light is absorbed using the wave picture. This is one reason that the particular picture is useful. In order to combine the wave and particle pictures we often speak of a wave packet.
