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Einstein won his Nobel Prize for
A. Theory of Relativity
B. Explanation of photoelectric effect
C. His theory of atomic heats of solid
D. None of the above

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Hint: Einstein’s theory of theory of relativity, explanation of photoelectric and theory of atomic heats of solids, all three are one of most famous theories. So research on all three of these theories, which may help to get to the answer.

Complete answer:
Einstein won his Nobel Prize for the explanation of photoelectric effect.
Hence, the correct answer is B. Explanation of photoelectric effect
Additional Information: Einstein won the Nobel Prize in physics for the year 1921 for his explanation of photoelectric effect. The photoelectric effect is a phenomenon due to which electrons are emitted from the surface metals when certain frequencies of light are incident upon it. Before Einstein, many had tried to explain the phenomenon but failed. Even Maxwell’s widely accepted Electromagnetic theory of light was unable to successfully explain the phenomenon. Einstein on the other hand used Planck’s idea of quantisation of light, i.e. the idea that light is a particle. He theorized that light is made up of particles (called quanta or photon). The energy carried by each particle is dependent on the light's frequency and is given by the equation, $E=h\nu $, (where h is Planck’s constant and $\nu $ is the frequency of light). When light is incident on the metal's surface, a part of the energy is used to release the electron from the atom and the rest of the energy is transferred to the electron as Kinetic energy.
Mathematically, this is written as
$E=W+KE$
$hv=W+KE$
$KE=hvw$
With this, Einstein was successfully able to explain the photoelectric effect using the particle nature of light.

Note: Here is a short on Einstein’s theory of relativity.
Theory of relativity is considered as one of the greatest revolutions. It changed everyone’s understanding on time. A basic consequence of this theory is that faster moving bodies travel into the future. The theory was composed on the assumption that speed of light is the fastest that a body can ever attain.