Let x be the uncertainty in the measurements of position and p the uncertainty in measurement of momentum. The…

Analyze the question: The question asks for the correct mathematical statement of Heisenberg's Uncertainty Principle, relating the uncertainty in position (Δx) and the uncertainty in momentum (Δp).

Concept: Heisenberg's Uncertainty Principle says we cannot measure both the exact position and the exact momentum of a particle at the same time. The more precisely one is known, the less precisely the other can be known. The product of the two uncertainties therefore has a minimum value:

Δx · Δp ≥ ħ/2, where ħ = h/2π

In many WASSCE and school textbooks, this is written in the simpler order-of-magnitude form:

Δx · Δp ≥ h

Working through the options:

• A (Δx·Δp = h): Wrong. The principle sets a lower limit, not an exact value.
• B (Δx·Δp ≤ h): Wrong. This would put an upper limit on the product, and the principle says the opposite.
• C (Δx·Δp ≥ h): Correct. The product can never be smaller than a minimum value of the order of h. This is the "greater than or equal to" form.
• D (Δx·Δp > h): This is close, but it excludes the equality case. The principle allows the product to reach the minimum value, so "≥" is the better statement.

Answer: Option C.

Exam tip: Remember that the uncertainty principle sets a minimum on the product of uncertainties. Both quantities cannot be made arbitrarily small together, so the sign is always "≥" and never "≤".