The Heisenberg Uncertainty Principle is a fundamental principle in quantum mechanics, based on which it is impossible to know at the same time with infinite precision certain pairs of physical properties of a particle, for example, the position and the momentum of the particle. It greatly changes our view of the microscopic world.

What is the Heisenberg Uncertainty Principle?

German physicist Werner Heisenberg formulated the uncertainty principle in 1927. The uncertainty principle says that it is impossible to precisely measure, at the same time, both the position and momentum of any particle. The more accurately we know one of these quantities, the less accurately we can know the other. This is not because equipment for measurement has limitations but because of a basic property of quantum systems.

Formula 

Heisenberg Uncertainty principle formula is expressed as,

where,

• h = Planck's constant ( 6.62607004 × 10-34 m2 kg /s)

• Δp is the uncertainty in momentum

• Δx is the uncertainty in position

Solved Example

Heisenberg Uncertainty Principle Problems 

We will go through the questions of Heisenberg Uncertainty principle.

Problem 1: The uncertainty in the momentum Δp of a ball travelling at 20 m/s is 1×10−6 of its momentum. Calculate the uncertainty in position Δx? Mass of the ball is given as 0.5 kg.

Solution:

 Known numerics are,

 v = 20 m/s,

 m = 0.5 kg,

 h = 6.62607004 × 10-34m2 kg / s

Δp =p×1×10−6

As we know that,

P = m×v 

   = 0.5×20 

   = 10kg m/s

Δp = 10×1×10−6

Δp = 10-5

The Heisenberg Uncertainty principle formula is :

 

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