In quantum mechanics the product of the uncertainty in position times the uncertainty in velocity must be
A) smaller than Planck's constant divided by mass.
B) larger than Planck's constant divided by mass.
C) equal to Planck's constant divided by mass.
D) added to Planck's constant divided by mass.
E) larger than Planck's constant multiplied by mass.

Question

Quizplus · Accepted Answer

The Heisenberg Uncertainty Principle in quantum mechanics states that the product of the uncertainty in position ($\Delta x$) and the uncertainty in momentum ($\Delta p$) (not velocity, but often related through $p = mv$) is greater than or equal to half of the reduced Planck's constant ($\hbar$), i.e., $\Delta x \Delta p \geq \frac{\hbar}{2}$. Since the reduced Planck's constant ($\hbar$) is related to the Planck's constant ($h$) by $\hbar = \frac{h}{2\pi}$, the principle implies that the product of uncertainties is inherently constrained by the nature of quantum mechanics, not directly by mass as the options might suggest. However, the closest correct interpretation given the options is that the product of uncertainties must be larger than a quantity related to Planck's constant, acknowledging that the relationship involves Planck's constant and not its division by mass.

In Quantum Mechanics the Product of the Uncertainty in Position