The branch of science that takes into account this dual behaviour of matter is called quantum mechanics. Quantum mechanics is a theoretical science that deals with the study of the motion of the microscopic objects that have both observable wave like and particle like properties. This science was developed independently by Werner Heisenberg and Erwin schrodinger.
The direct and most important consequence of Heisenberg's uncertainty principle is its inability to determine the exact position of an electron in an atom when the energy of an electron is fixed and vice versa. Hence, we can only predict the probability of finding an electron in space around the nucleus and not its exact position.
The wave equation developed by Erwin Schrodinger provides a satisfactory description of an electron in an atom in these terms. Schrodinger won Nobel prize in physics in 1933 for this contribution to science. This wave equation formed the basis for the modern quantum mechanical model of the atom. The theory explains the dynamical properties of the microscopic particles in motion with high speed in terms of the wave nature of the particles. The most general form of the schrodinger's equation
1. The energy of electrons in an atom is quantized (it can only have certain specific values).
2. The existence of quantized electronic energy levels is a direct result of the wave like properties of electrons and are allowed solution of schrodinger wave equation.
3. All the information about the electron in an atom is contained in its orbital wave function '`psi`' and quantum mechanics makes it possible to extract this information from '`psi`'.
4. The path of the electron can never be determined accurately. Therefore, we find only the probability of the electron at different points in space around an atom.
5. The probability of finding an electron at a point within an atom is proportional to the square of the orbital wave function i.e., |`psi`|2 at that point. |`psi`|2 is known as probability density and is always positive. From the value of |`psi`|2 at different points within the atom, it is possible to predict the region around the nucleus where electron will most probably be found.