Physical concept of uncertainty principle

The physical concept of uncertainty principle become illustrated by considering an attempt to measure the position and momentum of electron moving in Boh'r orbit. To locate the position of the electron, we should devise an instrument 'super microscope' to see the electron. A substance is said to be seen only it could reflect light or any other radiation from its surface. Because the size of the electron is too small, its position at any instant may determined by super microscope employing light of very small wavelength (such as x-rays). A photon of such a radiation of small l, has great energy and therefore has quite large momentum. As one such photon strikes the electron and is reflected, it instantly changes the momentum of electron. Now the momentum gets changed and becomes more uncertain as the position of the electron being determined.

Application of Uncertainty principle: Several phenomenons in the case of particles of atomic dimensions can be understood in terms of the uncertainty principle. Few of them are as below:

1. It easily follows from the uncertainty principle that electrons cannot exist with in the nuclei of the atom.

2. The principle helps us to know that limit to the accuracy with which we can measure the frequency of the radiation emitted by an atom.

Numerical work out:

An electron has a velocity of 600 m/s² with an accuracy of 0.005%. Calculate the certainty with which the position of the electron can be determined. ( h = 6.6 x10-34Js, m = 9.1x10-31 kg)

Solution:

Given Δv = 

Now, Dx = ?

Again: we know

A microscope using photons is employed to locate an electron in an atom to with in a distance of 0.2ºA. What is the uncertainty in the momentum of the electron located in this way?

Solution:

Δp = ?

Δx = 0.2ºA = 0.2x10^-10m

According to Heisenberg principle