Blackbody radiation:
All objects emit thermal radiation. If the temperature of the object is sufficiently high, the radiation can be felt on one's skin and if the temperature is even higher then part of the radiation will be visible light. For example, lava from a volcano can glow red. This radiation is called blackbody radiation. If the temperature of the object is held constant, then the intensity of heat radiation can be plotted as a function of its wavelength, giving a graph of a characteristic shape, called the blackbody spectrum (see figure of a blackbody spectrum). Classical physics was unable to explain these graphs. In fact, it predicted that they would diverge for short wavelengths! This dramatic failure of classical physics was what prompted Max Planck to introduce quantum theory.
Stability of atoms:
In the early 20th century, physicists thought of an atom as a miniature solar system, with electrons orbiting a central nucleus. This analogy predicted, however, that an electron would be unable to stay in its orbit and would very quickly crash into the nucleus. In other words, classical physics predicted that atoms were unstable and hence could not be the building blocks of matter.
Line spectra of atoms:
In the 19th century, physicists observed that when a sample of a single element (e.g. sodium) was heated it emitted light, but only with a number of characteristic wavelengths, forming what is called a line spectrum. Classical physics was unable to explain this phenomenon. The banner on the page entitled "What is Quantum Theory?" shows the line spectrum of nitrogen.
Radioactive decay:
Radioactive decay, first observed in 1896, is the process whereby an unstable atomic nucleus loses energy by emitting particles or photons, thereby transforming itself into a nucleus of a different type. One of the earliest known examples is described schematically as follows:
226Ra → 222Rn + 4He
In words, a radium-226 nucleus emits a helium-4 nucleus (also called an α-particle) and is converted into a radon-222 nucleus.
Photoelectric effect
It was discovered in the 19th century that light falling on a metallic surface (e.g. sodium) causes electrons to be released, resulting in an electric current. A puzzling feature of this phenomenon, called the photoelectric effect, is that the energy of the electrons is determined by the wavelength of the light. Increasing the intensity of the light increases the number of electrons that are released, but not their energy. Classical physics predicted, erroneously, that the energy of the released photons would be proportional to the intensity of the incident light. Einstein received (his only) Nobel prize for applying quantum theory to explain the photoelectric effect.