Quantum Mechanical Model of the Atom

Two new theories came to substantially modify Bohr's Atomic model. They are:

Wave nature of material objects

In 1924, de Broglie's suggested that all material objects including an electron have a dual character; they behave as particles as well as waves. The wavelength associated with a particle of mass 'm', moving with velocity 'v' is given by de Broglie's relation as:

The discovery of the wave like character of the electron helped in the making of the modern electron microscope.

Heisenberg's uncertainity principle

Heisenberg, in 1927 pointed out that it is not possible to measure simultaneously both the momentum (or velocity) and the position of a microscopic particle with absolute accuracy. Mathematically this may be expressed

Dp = uncertainity in momentum

The constant on the right side of the equation (the product of the two uncertainties) tells us that the two uncertainties are inversely related. If the momentum of the particle is measured with more accuracy there will be a large uncertainity in its position and vice versa.

Uncertainity is not due to the lack of refined techniques available, but because we cannot observe microscopic bodies without disturbing them. [Observations made as result of the impact of light suffer a change in the position or velocity of these microscopic objects]. This does not hold good for large objects of daily light, as the changes that occur are negligible.

Probability picture of an electron

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.