By the end of the 19th century, physics was sorted. We had Newton's laws to explain the motion of objects around us, Kepler's laws to explain the motion of planets around the Sun, we could explain the waves on strings, the ripples in the pond, and we had even derived the relationship between electricity and magnetism. All this, because of a carefully devised set of laws known as classical physics.
But, classical physics could not explain a new problem nature thre at us - black body radation spectrum.
According to Kirchhoff's laws, every object, at every temperature, emits electromagnetic radiation and also emit the radiation that falls on them. There are some good absorbers and then there are some bad absorbers of radiation. A blackbody is a perfect absorber and a perfect emitter of radiation.
Perfect blackbodies do not exist in nature - we only have approximations. The Sun is a blackbody, stars are blackbodies, and even a light bulb can be considered to be a blackbody. The blackbody spectrum is a curve between the energy density of the radiation and its frequency or wavelength. Classical physics could not explain the shape of the blackbody spectrum.
There are two experimental laws associated with a blackbody. The first is the Wein's displacement law. It states that the temperature at which the peak energy density of blackbody radiation is inversely proportional to the wavelength. The second law is the Stefan's law. It states that the total energy output of a blackbody, or the total luminosity is proportional to the fourth power of temperature of the blackbody. Stefan's law has many applications in astronomy.
The first attempt to explain the spectrum was made by Wilhelm Wein. He gave the Wein's distrubution law, an empirical formula that could only explain the curve at high frequencies.
The second attempt was made by Rayleigh and Jeans. They considered blackbody radiation to be made of standing waves inside a cubical box. Using classical statistical mechanics, they calculated the number of modes of vibrations or the number of standing waves inside a frequency interval. They associated average energy to each of the standing waves - kT where k is the Boltzmann's constant and T is the temperature.
By multiplying this average energy with the number of modes, we get the energy density - the Rayleigh-Jeans law. However, the Rayleigh - Jeans law can only explain the black body spectrum at low frequencies. It blows up at high frequencies. This is known as the Ultraviolet Catastrophe.
The black body spectrum was finally explained by Max Planck using quantum physics.