Uncertainty Principle Using ΔPΔx ≥ H/2: a Small Dust Particle

question 24

Essay

Uncertainty principle using ΔpΔx ≥ h/2: A small dust particle of mass 7.90 × 10^-6 g is being observed under a magnifying lens. Its position is determined to within 0.0050 mm. (1 y = 3.156 × 10⁷ s, h = 6.626 × 10^-34 J ∙ s)
(a) Find the minimum uncertainty in its velocity implied by the uncertainty in its position.
(b) Assuming the dust particle is moving at the speed you just found, how many years would it take for the particle to move 1.0 mm?

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Definitions:

Value

The worth, importance, or usefulness of something, often measured in terms of money, utility, or general significance.

Normal Random Variable

A variable following a normal distribution, characterized by a symmetric bell-shaped curve.

Variance

A measure of the dispersion or spread of a set of data points around their mean value, indicating the degree of variation from the average.

Probability Distribution

A statistical function that defines the possible values and likelihoods that a random variable can take within a given range.