This motivating puzzle concerned blackbody radiation,
the electromagnetic radiation given off by a hot, glowing coal
that absorbs all the light that falls onto it (thus appearing black).
This radiation was studied by measuring its spectrum, the amount
of energy of any given frequency emitted when the object was heated
to a certain temperature. By the end of the nineteenth century,
German experimentalists had studied this spectrum and found that
for any given temperature, there was a rapid rise in the intensity
of the emitted radiation as the frequency increased, followed by
a rapid decline. The characteristic shape of this curve, which
was always independent of the type of object being heated, was
reproduced theoretically by the physicist Max Planck. However,
Planck was unable to explain the shapes of these curves using either
statistical mechanics and the corresponding thermodynamics, or
electromagnetism. The only way for Planck to account for the shape
of the curves was by positing that the radiation was emitted in
discrete particles, called "quanta." Planck formulated the equation
*E* = *hf*, in which the energy (*E*)
emitted by a blackbody at a given temperature is equal to the frequency
of light involved (*f*) multiplied by a new universal physical
constant soon named "Planck's constant" (*h*).
However, Planck did not realize the ramifications of his own formula,
viewing it as nothing more than a mathematical device to explain
the radiation curve; it was Einstein, in 1905, who explained Planck's
law as a fundamental statement about the nature of light and its
interactions with matter.

In his 1905 paper, Einstein demonstrated that light could only be emitted or absorbed in finite, discrete units. This idea challenged the standard physical theory of the time, according to which light was a continuous wave. In the 1860s and 1870s, James Clerk Maxwell had shown that light is a wave of electric and magnetic fields and that atoms absorbed or emitted light waves in a continuous fashion. However, Einstein showed that the continuous waves of Maxwell's equations could be considered only averages over all the light quanta emitted or absorbed.

Einstein used his light-quantum hypothesis to explain another important puzzle, the photoelectric effect. This experimental phenomenon involves the ejection of electrons from a metal irradiated by light. In the experiment, light of various frequencies is shone on the metal. Once a certain threshold frequency is reached, the metal ejects electrons in response. The energy of these electrons rises linearly (in a curve) with the frequency of the incident light. The resulting curve is independent of the intensity (brightness) of the incident light. These results could not be explained according to traditional wave theory because according to this view, the energy of light is proportional to its intensity, so the energy transmitted to the ejected electrons should be proportional to intensity rather than frequency. Moreover, according to the traditional view, there should not be a threshold frequency needed to eject the electrons; a bright enough light of low frequency should be enough to eject electrons. However, Einstein explained that if light is considered as composed of discrete particles (later called "photons"), then each photon would carry a definite amount of energy that was then imparted to the ejected electron. Moreover, the energy of an incoming photon would have to be great enough to eject an electron in the first plaace, resulting in a frequency threshold. Thus, Einstein was able to provide a theoretical explanation for the energy-versus-frequency graph of the photoelectric effect.

When Einstein first introduced his photon idea in 1905, he called it merely a "heuristic" that was useful in explaining the photoelectric effect. He emphasized that while some phenomena required a particulate interpretation, many could still be explained using the wave interpretation. However, in a series of subsequent papers published in 1906 and 1907, Einstein used his statistical mechanics to propose the existence of light quanta. For the rest of his scientific career, he explored the significance of the resulting wave-particle duality in terms of his search for a fusion (or unity) of the wave and particle aspects of electromagnetism. First, however, he published another great 1905 paper, which is the subject of the next section.