Probability concept

According to Heisenberg's uncertainty principle, it is impossible to describe the exact position of an electron at a given moment in terms of position, we can speak of most probable regions where the probability of finding an electron in the space around the nucleus of an atom is high. The electron does not always remain at a fixed distance from a nucleus. It keeps moving in the whole space around the nucleus but tends to remain most of the time within a small volume around the nucleus, where the probability of locating the electron is maximum.

A new atomic model, was needed to explain

• Wave nature (dual character) of atoms.

• The idea of uncertainity in the position of electrons in a atom.

• Concept of fixed energy states.

Schrodinger put the wave model or quantum mechanical model of atom forward. The behavior of an electron is defined by the mathematical representation:

where,

y = (psi) is a wave function of space coordinates 'x', 'y', 'z' and represents the amplitude of the electron wave.

m = mass of the electron

E = the total permissible energy level, which the electron can have.

V = potential energy of the electron given by ze²/r.

h = Planck's constant having the value 6.626 x 10^-34 J s.

d= (delta)stands for infinitesimal change.

The wave length function y (psi) describes a number of possible states of an electron in an atom. Since a large number of solutions are possible, four quantum numbers were introduced, which describe meaningful permissible values of energy and location with respect to its nucleus.