Uncertainty Principle Using ΔXΔp ≥ ħ: a Small Dust Particle

question 54

Essay

Uncertainty principle using ΔxΔp ≥ ħ: 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 × 10^{7 s}, ħ = 1.055 × 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:

Price-Earnings Ratio

A valuation measure comparing the current share price of a company to its per-share earnings, used to evaluate if a stock is over or undervalued.

Retained Earnings

The portion of a company's profits that is kept or retained and not paid out as dividends to shareholders.

Selling Bonds

The act of offering bonds to investors as a way to raise funds; bonds are debt securities under which the issuer owes the holders a debt.

Shares of Stock

Units of ownership interest in a corporation or financial asset that provide for an equal distribution in any profits, if any are declared, in the form of dividends.