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Module 1 : Atomic Structure

Lecture 1 : Structural Chemistry

1.7

The Uncertainty Principle
In the newer and more accurate theory of matter given by Heisenberg, Schrödinger and Dirac, the description of matter is not based on the simultaneous specification of positions and momenta of particles. This implies that we cannot speak of the trajectories of these subatomic particles at all. Indeed, the Heisenberg uncertainty principle states that the position and the momentum of a particle cannot be determined simultaneously and the product of the uncertainty of the position and the uncertainty of momentum is given by

	(1.2)
Here the motion has been considered only in the x-direction.
There is thus a fundamental difference in the description of observables such as position, momentum and even others such as energy. The uncertainty in position is akin to the error in measuring the position and can be taken as the root mean square deviation in the position of the particle which is given by


where the angular brackets < > refer to the average values.

The new description of matter can be formulated in terms of postulates or laws, which will replace Newton's laws. The new description goes over to or becomes equivalent to the classical description when the particle size is “macroscopic”, e.g., 0.01g or greater in mass. These postulates are summarized in the next paragraph. You may wonder about the justification of these seemingly strange postulates. The final justification is the agreement of the results of the theory with experiments. We are forced to seek these and other newer descriptions whenever old laws such as Newton's laws fail to explain phenomena involving electrons, atoms and molecules and other microscopic objects such as protons, neutrons, photons and so on. If the new description fails to explain all the observed phenomena, we have no choice but to replace the new postulates by more appropriate laws as and when they are discovered. It turns out that with the present postulates, a fairly accurate description of molecular structures can be obtained.