The laws of classical mechanics, which encompass enough physics to send man to moon, failed to comprehend the peculiar behavior of the atomic and sub-atomic world. One such peculiarity is the wave-particle duality. American physicists Davisson and Germer performed an experiment to prove that electrons behave like waves. A beam of light focused onto crystalline surface shows diffraction pattern, a property generally associated with waves. Davission and Germer used a beam of electrons fired from an electron gun and focused them on a nickel surface. Surprisingly, electron beam behaved exactly like light waves and showed diffraction pattern. Electron microscopes that are used to study the nano-sized world are constructed based on the wave like behavior of electrons.
Wave theory states that energy of a wave is associated with its intensity, as discussed in A Level Physics tuition classes; an increase in the intensity of the wave results in an increase in its energy. Electrons bound in an atom can be excited and liberated by shining light on them. Photoelectric effect comprises an observation that electrons are emitted from the metal surface when it is shone by a light beam. A common expectation is, electrons that are tightly bound need more energy to be emitted from the metal surface and hence a light beam of higher intensity should suffice the need. But the experimental evidences spoke otherwise; an increase in intensity of light did not affect the electron excitation but an increase in its frequency did. The dependency of electron excitation on the frequency of the light shone cannot be deduced from the wave theory of light. Albert Einstein later explained this astonishingly counter-intuitive observation by assuming that light exists in the form of particles called as photons. It was theorized that the energy of a photon is proportional to the frequency of light and hence the excitation of electrons is a function of the frequency of light used.
Wave-like-behavior of particles and the particle-like-behavior of waves is popularly known as wave-particle duality. Wave-particle duality remains a puzzle unsolved in the classical mechanics paradigm. Quantum mechanics was formulated to explain these seemingly mysterious phenomena. One of the basic assumptions of quantum mechanics is that a particle does not follow a specific path in space but is distributed in the space, just like a wave. A given point in space is tagged with a number, which is the probability of finding a particle at that point in space. This number is obtained from a function called as wave function, denoted by Psi.
Psi at a given point squared and multiplied with the tiny volume surrounding the point yields probability; and the probability density is the square of Psi. Psi varies with space i.e., Psi can have different values at different points in space. Psi also depends on time, at any given point in space Psi can have different values at different times. The triumph of quantum mechanics is in explaining phenomena like tunnelling, a process in which a particle crosses an energy barrier which is much larger than the energy it possess. This phenomenon can be explained by calculating the value of Psi on the other side of the barrier and if the probability density has definite value, though minute, the particle can cross the barrier and exist on the other side.
At the same time, quantum tunnelling is the driving factor that enables nuclear fusion in sun and hence sustains the existence of life.