Question

uncertainty principal numercal​

Answer 1

The uncertainty in position is the accuracy of the measurement, or Δx=0.0100nm Δ x = 0.0100 nm . Thus the smallest uncertainty in momentum Δp can be calculated using ΔxΔp≥h/4π Δ x Δ p ≥ h / 4 π . Once the uncertainty in momentum Δp is found, the uncertainty in velocity can be found from Δp=mΔv Δ p = m Δ v .

Answer 2

Explanation:

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,

Heisenberg Uncertainty Principle Formula 1

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 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.

Answer:

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