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Einstein's mass-energy equivalence principle led to the understanding that a large amount of energy could be released from a small amount of matter, as is the case in nuclear fission and fusion. This concept laid theoretical foundations for the development of nuclear power and weapons.

Mass-energy equivalence is encapsulated by the equation $E = mc^2$, which states that energy can be converted into mass and vice versa. This principle is a central tenet of the Special Theory of Relativity and has significant implications for nuclear and particle physics, such as the production of energy in nuclear reactions.

The photoelectric effect is the emission of electrons from a material when light is shone upon it. Einstein explained this effect by proposing that light is made of individual quanta, later called photons, which carry energy that is absorbed by the electrons. This work challenged the classical wave theory of light and marked a fundamental contribution to the birth of quantum mechanics.

Einstein wrote a letter to U.S. President Franklin D. Roosevelt in 1939, co-signed by fellow physicist Leo Szilard, warning about the potential development of extremely powerful bombs of a new type, based on nuclear chain reactions in uranium. This letter led to the U.S. government's serious efforts to investigate nuclear weapons, culminating in the Manhattan Project.

Einstein introduced the cosmological constant as a term in his field equations for General Relativity, as a way to achieve a static universe, which was the prevailing belief at the time. After the discovery of the expanding universe, he allegedly called this his 'biggest blunder.' However, the concept has regained attention with the discovery of dark energy accelerating cosmic expansion.

Einstein spent much of his later years attempting to develop a unified field theory, which aimed to describe the fundamental forces of nature by a single theoretical framework. Despite his efforts, he did not succeed in his lifetime, and the quest for a unified theory continues in modern physics.

Einstein proposed the Special Theory of Relativity in 1905, which introduced the famous equation $E = mc^2$. The theory revolutionized the concepts of space, time, and energy, asserting that the laws of physics are the same for all non-accelerating observers, and that the speed of light in a vacuum is constant, irrespective of the motion of the light source.

Albert Einstein was awarded the Nobel Prize in Physics in 1921 for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect, which was pivotal in establishing the theory of quantum mechanics. His work on the photoelectric effect demonstrated that light could be described as both a wave and a particle, known as wave-particle duality.

Einstein proposed the idea of light being composed of quanta (photons) which carry energy that is proportional to the frequency of light. This was a fundamental step for the quantum theory of light, which contributed to the development of quantum mechanics.

The General Theory of Relativity, formulated between 1907 and 1915, is a theory of gravitation that describes gravity not as a force, but as a consequence of the curvature of spacetime caused by the uneven distribution of mass. This theory has been confirmed by numerous experiments and has crucial implications for astrophysics, including the study of black holes and the expansion of the universe.

In 1905, Einstein explained Brownian motion as the erratic random movement of pollen particles in a fluid, caused by the collision with fast-moving molecules of the fluid. This provided empirical evidence for the atomic theory, confirming the existence of atoms and molecules.