The dual nature of matter imposes a limitation on the simultaneous determination of position and velocity of a microscopic particle.

**Heisenberg’s
uncertainty principle**

The dual nature of matter imposes a limitation on the
simultaneous determination of position and velocity of a microscopic particle.
Based on this, Heisenberg arrived at his uncertainty principle, which states
that ‘It is impossible to **accurately**
determine both the position as well as the momentum of a microscopic particle **simultaneously**’. The product of
uncertainty (error) in the measurement is expressed as follows.

Δx.Δp ≥ h/4π -------- (2.11)

where Δx and Δp are uncertainties in determining the
position and momentum, respectively.

The uncertainty principle has negligible effect for
macroscopic objects and becomes significant only for microscopic particles such
as electrons. Let us understand this by calculating the uncertainty in the
velocity of the electron in hydrogen atom. (Bohr radius of 1^{st} orbit
is 0.529 Ǻ) Assuming that the position of the electron in this orbit is
determined with the accuracy of 0.5 % of the radius

Uncertainity in position = ∆x

From the Heisenberg’s uncertainity principle,

Therefore, the uncertainty in the velocity of the electron
is comparable with the velocity of light. At this high level of uncertainty it
is very difficult to find out the exact velocity.

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