# Heisenberg Uncertainty Principle Formula

Quantum mechanics is the discipline of measurements on the minuscule scale. That measurements are in macro and microphysics can lead to very diverse consequences. Heisenberg uncertainty principle or basically uncertainty principle is a vital concept in Quantum mechanics. The uncertainty principle says that both the position and momentum of a particle cannot be determined at the same time and accurately. The result of position and momentum is at all times greater than h/4π. The formula for Heisenberg Uncertainty principle is articulated as,

$\Delta x\Delta p\geq \frac{h}{4\pi }$

Where

h is the Planck’s constant ( 6.62607004 × 10-34 m2 kg / s)

Δp is the uncertainty in momentum

Δx is the uncertainty in position

Heisenberg Uncertainty Principle Problems

We’ll go through the questions of the Heisenberg Uncertainty principle.

## Solved Examples

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

Known numerics are,
v = 20m/s,

m = 0.5kg,

h = 6.62607004 × 10-34 m2 kg / s

Δp =p×1×10−6

As we know that,
P = m×v = 0.5×20 = 10kgm/s
Δp = 10×1×10−6

Δp = 10-5
Heisenberg Uncertainty principle formula is given as,

$\Delta x\Delta p\geq \frac{h}{4\pi }$

$\Delta\,&space;\times\,&space;\geq&space;\,&space;\frac{h}{4\pi&space;\Delta&space;p}$

$\Delta\,&space;\times\,&space;\geq&space;\,&space;\frac{6.626\times&space;10^{-34}}{4\times&space;3.14\times10^{-5}&space;}\,&space;=0.527\,&space;\times\,&space;10^{-29}m$