Heisenberg Uncertainty Principle Formula, Calculation of Uncertainty Position

Heisenberg Uncertainty Principle Formula

Quantum mechanics is a branch of science that deals with measurements on the smallest scale. Those measurements are useful in both macro and microphysics and lead to very different results.

The Heisenberg Uncertainty Principle or simply the uncertainty principle is a very important concept in quantum mechanics. Uncertainty is a very inherent property of nature. Therefore, we can conclude that both position and velocity of a particle cannot be accurately determined simultaneously.

Heisenberg Uncertainty Principle Formula Is  Given By,

Δx Δp  ≥   h 4π

Where,

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

Δp is the uncertainty in momentum

Δx is the uncertainty in position

Sample Problems

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.

Solution

Known numerics are,

v = 30 m/s,

m = 0.6 kg,

h = 6.62607004 × 10-34 m2 kg / s

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Δp =p×1×10−6

As we know that,

P = m×v

= 0.6×30

= 18kg m/s

Δp = 18×1×10−6

Δp = 18-5

Heisenberg Uncertainty principle formula is given as,

Δx Δp  ≥   h4π

Δx  ≥   h/ 4π Δp

Δx  ≥   6.626 ×10-34 / 4 × 3.14 × 18-5

                                              = 0.520 × 10-29 m.

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