In 1900, Max Planck announced his derivation of the black-body radiation law: this was based on the revolutionary idea that the energy emitted by a resonator could only take on discrete values or quanta. The value of energy for a given resonator frequency v is E=hv where h is a universal constant, now called Planck's constant.
http://physicsweb.org/articles/world/14/12/7
Einstein's special theory of relativity describes the motion of particles moving at velocities close to the speed of light.
Einstein's theory of special relativity is based on two principles - the two basic postulates of special relativity:
1. The speed of light is the same for all observers, no matter what their relative speeds are.
2. The laws of physics are the same in any inertial (that is, non-accelerated) frame of reference. This means that the laws of physics observed by a hypothetical observer travelling with a relativistic particle must be the same as those observed by an observer who is stationary in the laboratory frame.
Consequences of these assumptions are surprising, like for example time dilation for moving objects confirmed in 1941 by B. Rossi and D. B. Hall in measurements of cosmic-ray muon decay.
(http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muonex.html)
Probably the most famous scientific equation of all time, was derived by Einstein in 1905 is the relationship E = mc2.
The photoelectric effect involves the emission, or release, of electrons from the surface of a conductor when the surface of the conductor is illuminated by light (usually UV).
According to the classical Maxwell wave theory of light, the more intense the incident light the greater the energy with which the electrons should be released from the conductor. That is, the average energy carried by an ejected electron should increase with the intensity of the incident light.
Following the experiments carried out between 1902-03 Philipp Lenard found out that classical Maxwell wave theory did not explain the photoelectric effect. Lenard discovered that the energy of emitted electrons is independent from the intensity of the incident radiation but depends on a type of the lamp used (Zn arc or carbon arc lamp).
A. Einstein (1905) successfully resolved this paradox by proposing that the incident light consisted of individual quanta, called photons, that interacted with the electrons in the metal like discrete particles, rather than as continuous waves. For a given frequency, or 'colour,' of the incident radiation, each photon carried the energy
E = hn, where h is Planck's constant and n
is the frequency. Increasing the intensity of light corresponded, in Einstein's model, to the increasing the number of incident photons per unit time (flux), while the energy of each photon remained the same (as long as the frequency of the radiation was held constant).
There are a striking similarities between the Gaussian distribution and the `drunken sailor' staggering, or Brownian motion. This phenomenon was first observed by a botanist named Brown who watched small particles moving in water. It is very likely that what he observed could have been the vibrations of the apparatus and not ‘Brownian motion’, but the name has stuck and the phenomenon is ‘real’. The theory was formally developed by Einstein and the Polish scientist Smoluchowski at about the same time. It led to the first truly convincing demonstration of the atomic theory of matter and a fairly precise determination of Avogadro's (Loschmidt) number.
http://www.physicstoday.org/pt/vol-54/iss-3/p45.html
Minkowski developed a new view of space and time and laid the mathematical foundation of the theory of relativity. Important, formal contributions to the special relativity theory came also from Henri Poincaré.
http://www-cosmosaf.iap.fr/Poincare-RR3A.htm
The Danish astronomer E. Hertzsprung and the American astrophysicist H. Norris Russell (below) correlate the energy emitted by a star with its temperature. This orders stellar types from red giants to white dwarfs, and leads to understanding how stars were born and die.