Which of the following pairs of concepts constitutes complementary variables as expressess by the Heinsberg uncertainty principle?

Analyze the question: The question asks which pair of quantities are complementary variables in the Heisenberg uncertainty principle (the question spells it "Heinsberg"). Complementary variables are pairs that cannot both be measured with perfect precision at the same time.

Explain the concept: The Heisenberg uncertainty principle says that the more precisely you know one quantity in the pair, the less precisely you can know the other. The best-known pair is position and momentum:

Δx · Δp ≥ h/4π (or ħ/2)

where

• Δx = uncertainty in position
• Δp = uncertainty in momentum
• h = Planck's constant

The other well-known pair is energy and time:

ΔE · Δt ≥ h/4π

Check each option:

• A. Momentum and time: Not a conjugate pair. Momentum pairs with position, and time pairs with energy.
• B. Energy and acceleration: Not a conjugate pair. Acceleration plays no role in the principle.
• C. Position and momentum: This is the classic complementary pair in the principle. ✔
• D. Velocity and momentum: These are directly related by p = mv, so knowing one gives you the other. They are not complementary.

Answer: The correct option is C. Position and momentum.

Exam tip: Remember the two pairs as "x-p" and "E-t". If an option has position with momentum (or energy with time), pick it. Be careful with velocity and momentum, because they are proportional and so are not complementary.