# 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 $\Delta$x and $\Delta$p represent the uncertainties in the position and momentum respectively. Then according to Heisenberg

$\Delta$x . $\Delta$p  $\geq$ $\frac{h}{4\pi}$ ………….. (1)

The product of uncertainties in position ($\Delta$x) and momentum ($\Delta$p) 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$$\times$ m ($\Delta$v) $\geq$ $\frac{h}{4\pi}$ $=$ $\Delta$$\times$ $\Delta$$\geq$  $\frac{h}{4\pi&space;m}$

If the position is determined accurately  $\Delta$x = 0 and $\Delta$v = $\alpha$. That means the inaccuracy in measuring the velocity is $\alpha$. If velocity is determined accurately $\Delta$v = 0 and $\Delta$x = $\alpha$.

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.