Heisenberg’s uncertainty principle

Heisenberg’s Uncertainty principle : “Simultaneous and exact determination of the position and momentum of a sub-atomic particle, like electron moving with high speed is impossible”.

If \Deltax and \Deltap represent the uncertainties in the position and momentum respectively. Then according to Heisenberg

\Deltax . \Deltap  \geq \frac{h}{4\pi} ………….. (1)

The product of uncertainties in position (\Deltax) and momentum (\Deltap) of an electron cannot be less than \frac{h}{4\pi}.  It can be equal or greater than \frac{h}{4\pi}.

Since momentum = mass \times velocity,  the equation (1) can be written as

\Delta\times m (\Deltav) \geq \frac{h}{4\pi} = \Delta\times \Delta\geq  \frac{h}{4\pi m}

If the position is determined accurately  \Deltax = 0 and \Deltav = \alpha. That means the inaccuracy in measuring the velocity is \alpha. If velocity is determined accurately \Deltav = 0 and \Deltax = \alpha.

Significance of Heisenberg’s Uncertainty principle :

  • This principle rules out the existence of definite paths or trajectories of electrons and other similar particles.
  • This principle is significant only for the motion of microscopic objects and is negligible for that of macroscopic objects.
  • In dealing with milligram size or heavier objects, the associated uncertainties are hard of any real consequence.