Which principle states you cannot know both position and velocity exactly at the same time?

• A. Quantum numbers
• B. Heisenberg uncertainty principle
• C. Ground state
• D. Quantum theory

Answer: (B)

At the heart of this question is the idea that at the quantum scale there is a fundamental limit to knowing a particle's position and its momentum (and thus velocity) simultaneously. This limit is formalized in the Heisenberg uncertainty principle, which states that the uncertainties in position and momentum obey Δx Δp ≥ ħ/2. Because momentum p equals mass times velocity for non-relativistic particles, this relation translates into a limit on how precisely velocity can be known when position is known, and vice versa. This is not due to imperfect instruments; it's a property of quantum systems themselves, arising from the wave-like nature of matter and the mathematics of quantum states. The other terms describe different quantum concepts—quantum numbers label discrete energy or state values, the ground state is the lowest energy state, and quantum theory is the general framework—none express the specific limit on simultaneous precision of position and velocity.