The stages of the aging of a star are defined by the color of the star. When the star is young it has a yellowish color, like our sun. As the star ages it begins to expand and cool. The color shifts to the red. Eventually the star becomes a red giant. Finally, the begins to shrink again as the hydrogen fuel is burned up. Gravity plays a larger role at this stage. As the star shrinks it heats up and becomes a white dwarf. Even with primitive equipment one can determine that srars have a spectrum. It is somewhat asymmetric and its maximum depends on the temperature of the star. These facts were known in the late 19th century.
Empirical relationship between the absorption maximum and temperature
The relationship between the emission wavelength of an object and its temperature is also part of our common experience. If a metal is heated it eventually begins to glow with a reddish color. We say that it is "red hot". If we heat it further it can glow with a whiteish color and we call it "white hot". However, if you have an electric burner on a stove you can feel the infrared radiation with your hand before you can see the red color. This tells you that the burner emits infrared radiation before it reaches the red hot stage. There is a systematic change in the emission wavelength of the metal and the temperature. These observations are not just true for metals, but for every object in the universe. Infrared or "night" vision uses infrared detectors to see the contrast of objects of varying temperature. One see their infrared emission using that technology. Since the body tempeature of a human is 37 o<\super>C one can easily see a human against the background of the ambient, which will surely have a lower temperature. The empirical observations lead Wilhelm Wien to write down an equation that expresses this inverse relationship. The Wien displacement law even holds for the universe itself. Astrophysicists study the temperature of deep space using radiotelecopes to measure the radiation that reaches earth. That radiation has a thermal radiation curve like that observed for a stars and other objects, but it has very long wavelength consistent with a temperature of 2.7 K. Not surprisingly, the temperature of deep space is quite quite low. It's cold out there!.
The attempt to explain the Wien displacement law using Maxwell's equations was a failure. This attempt known as the Rayleigh-Jeans law gives a strange prediction that the emitted energy will increase without bound as the wavelength decreases. This is clearly not correct since it does not predict a thermal emission spectrum of the type that can be measured for the sun and other objects. The failure of classical physics is the starting point for quantum physics. But, in reality, the theory that replaced the Raleigh-Jeans law does not look at first like it is revolutionary, but it is.
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.
