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 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,

\(\begin{array}{l}\triangle x \triangle p \geq \frac{h}{4\pi } \end{array} \)

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 Example

Example 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.


Known numerics are,
v = 20 m/s,

m = 0.5 kg,

h = 6.62607004 × 10-34 m2 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
Heisenberg Uncertainty principle formula is given as,

\(\begin{array}{l}\triangle x \triangle p \geq \frac{h}{4\pi } \end{array} \)
\(\begin{array}{l}\triangle x \geq \frac{h}{4\pi \triangle p } \end{array} \)
\(\begin{array}{l}\triangle x \geq \frac{6,626\times 10^{-34}}{4 \times 3.14 \times 10^{-5} } = 0.527\times 10^{-29}m\end{array} \)

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