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Quantum Mechanical Model of Atom

QUANTUM MECHANICAL MODEL OF ATOM

The motion of all macroscopic objects such as a falling stone, moving car, orbiting satellite, etc., can be successfully described in terms of classical mechanics, based on Newton’s laws of motion. These objects have predominantly particle character. However, a microscopic object such as electron has both observable wave-like and particle-like properties. The behaviour of such particles cannot be explained on the basis of classical mechanics which is based on Newton’s laws of motion. In order to explain the behaviour of electrons and other microscopic particles a new branch of science called quantum mechanics was developed. Quantum mechanics is a theoretical science that takes into account the dual nature of matter. Quantum mechanics was developed independently in 1926 by Werner Heisenberg and Erwin Schrodinger.

Based on quantum mechanics a new model of atom was developed during 1920′s. This model is known as quantum mechanical model. In this model behaviour of the electron in an atom is described by an equation known as the Schrodinger wave equation.

The solutions of Schrodinger wave equation are known as wave functions (‘If). When Schrodinger wave equation is solved for hydrogen atom, several solutions are obtained. Out of these only certain solutions are permissible. Each permitted solution* or wave function corresponds to a definite energy state and is called orbital. Each energy state or orbital is characterized by a set of three quantum numbers, principal quantum number (n), azimuthal quantum number (l) and magnetic quantum number (m1). Each orbital can be considered as quantum mechanical analog of the electron orbits as proposed by Bohr. The electron orbitals in atoms are called atomic orbitals while those in a molecule are called molecular orbitals. Since in an atom (or a molecule) only specific or definite energy states are permitted, it implies that an electron in an atom (or a molecule) can have only certain specific values of energy. In other words, energy of electron in an atom is quantised.

SIGNIFICANCE OF ψ

A moving electron is associated with a wave and the wave function ‘If gives the amplitude of electron wave. It has got no physical significance. However, the square of ‘ψ i.e., | ψ|2  has a physical significance. Just like light radiations where square of amplitude gives the intensity of light, similarly, in electron wave ψ|2  gives the intensity of the electron at any point. In other words, the knowledge of ψ|2   is helpful in assessing the probability of electron in a particular region.

CONCEPT OF ORBITALS

According to Heisenberg’s uncertainty principle it is not possible to determine precisely the position and momentum of an electron in the atom simultaneously. Therefore, Bohr’s concept of well defined orbits is ruled out. In quantum mechanical model, we speak of probability or  possibility of  an electron with a particular energy being present in a certain region of space around the nucleus. The probability of finding the electron at a particular location is given by the square of wave function |ψ|2  corresponding to that location. There are certain regions around the nucleus where probability of finding the electron is high and there are certain regions where probability of finding the electron is low. The probability of finding the electron does not become zero even at large distances from the nucleus, although it may become negligible. Therefore, it is not possible to draw a boundary that will enclose the region of 100% probability. However, for the sake of simplicity we draw arbitrary boundaries which enclose the regions where probability of finding the electron is maximum (about 90-95%). These regions of space around the nucleus where probability of finding the electron is maximum are called orbitals.

An orbital may be defined as that region of space around the nucleus where the probability of finding an electron is maximum (90-95%).

It is rather difficult to represent an orbital by a simple picture. Different methods are employed for this purpose. But the most common method is to represent an orbital as a charge cloud in terms of small dots, the intensity of dots being more in some region and less in other.

In terms of charge cloud representation, the probability of finding an electron in a particular region of space is directly proportional to the density of dots in that region.

Fig. 5.23. Orbital and an orbit