NECO 2001 Physics · Question 11

Which statement is a correct consequence of the uncertainly principle?

Options

A.A particle’s kinetic energy cannot be measured accurately at any time
B.Both momemtum and energy of a particle can be known with absolute certainly
C.It is possible to measure exactly both the position and momentum of a particle at the same time
D.The complete knowledge of the position of a particle implies the complete ignorance of its energy
E.The uncertainty in our knowledge of energy and the duration taken to measure it, are each less than Planck’s constant.

Answer: D. The complete knowledge of the position of a particle implies the complete ignorance of its energy

Explanation written with AI and checked against the answer key

Analyze the question: You are asked which statement follows from the Heisenberg Uncertainty Principle.

Concept: The principle says certain pairs of quantities cannot both be known precisely at the same time:

Position and momentum: Δx · Δp ≥ h/4π
Energy and time: ΔE · Δt ≥ h/4π

If one quantity in a pair is known very precisely, the uncertainty in the other becomes very large.

Step-by-step check of the options:

A. Wrong. Kinetic energy can be measured accurately. The principle limits pairs of quantities, not a single measurement.
B. Wrong. It says momentum and energy can both be known with absolute certainty, but the principle limits precision for conjugate pairs (such as position and momentum), and this statement overreaches.
C. Wrong. This is exactly what the principle forbids. Position and momentum cannot both be measured exactly at the same time.
D. Complete knowledge of position (Δx → 0) forces Δp → ∞. Since kinetic energy is p²/2m, the uncertainty in momentum means the particle's energy is hugely uncertain.
E. Wrong. The principle says the product ΔE·Δt is at least of the order of Planck's constant (h/4π), not less than it.

Answer: Option D is the best choice. Precisely fixing position (Δx → 0) makes the momentum uncertainty enormous, and so the energy, which depends on momentum, becomes essentially unknown.

Exam tip: Remember "precise in one, fuzzy in the other." Any option claiming you can know both members of a conjugate pair exactly (C, B), or that the product of uncertainties is less than h (E), is wrong. Look for the option that says knowing one very well leaves the other very uncertain.

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