It is impossible to know exactly both the velocity and the position of a particle at the same time?

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

Answer: (B)

In quantum mechanics, you can’t know a particle’s exact position and exact velocity at the same time because of the Heisenberg Uncertainty Principle. It states that the uncertainties in position and momentum obey Δx Δp ≥ ħ/2. Since velocity is momentum divided by mass, a very precise position (tiny Δx) forces a large spread in momentum (a large Δp), making velocity highly uncertain. This arises from the wave nature of matter: localizing a particle in space corresponds to a wave packet with a broad range of momenta. The underlying math shows position and momentum operators do not commute, [x, p] = iħ, which enforces this fundamental limit. Other concepts like quantum numbers (discrete values of observables) or the ground state (a specific energy level) or quantum theory as a framework do not express this intrinsic limitation on knowing both quantities simultaneously.