# Heisenberg Uncertainty Principle Formula

## Heisenberg Uncertainty Principle Formula

Quantum mechanics is the discipline of measurements on the minuscule scale. That measurements are in macro and micro physics can lead to very diverse consequences. Heisenberg uncertainty principle or basically uncertainty principle is a vital concept in Quantum mechanics. Uncertainty principle says that both 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,

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

Where, the Planck’s constant (6.626×10−34×10−34Js) is h , Δp is the uncertainty in momentum and  Δx is the uncertainty in position

Heisenberg Uncertainty Principle Problems

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

Solved Examples

Problem 1: The uncertainty in the momentum Δp of a ball traveling at 20m/s is 1×10−6×10−6 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 = 6.626×10−34×10−34Js and

Δp = P×1×10−6×10−6

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

Δp = 10−510−5
Heisenberg Uncertainty principle formula is given as,

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

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

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

Problem 2: An electron in a molecule travels at a speed of 40m/s. The uncertainty in the momentum Δp of the electron is 10−610−6 of its momentum. Compute the uncertainty in position Δx if the mass of an electron is 9.1×10−319.1×10−31kg?

Given measurements are,
v = 40m/s, m = 9.1×10−31×10−31kg, h = 6.626×10−34×10−34Js and Δp = P×10−6×10−6
We know that,
P = m×v
P = 9.1×10−31×40=364×10−31×10−31×40=364×10−31kgm/s
Δp = 364×10−31×10−6= 364×10−37×10−31×10−6 = 364×10−37

Heisenberg Uncertainty principle formula is given as,

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

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

$\Delta\,&space;\times\,&space;\geq&space;\,&space;\frac{6.626\times&space;10^{-34}}{4\times&space;3.14\times364\times&space;10^{-37}&space;}\,&space;=1.44m$

#### Practise This Question

Separate the variables in the below given equation.

7x - 2y = 5xy

After separating the variables equation is of the form

72 = 5 * *