Because of Heisenberg's Uncertainty Principle,the velocity of a particle is known least precisely when the length of the wave packet representing the particle is A)

Question

Because of Heisenberg's Uncertainty Principle,the velocity of a particle is known least precisely when the length of the wave packet representing the particle is A)< 10 ^- ¹⁵ m. B)< 10 ^- ¹⁰ m. C)of the order of 1.00 m. D)>10 m. E)the length of a plane wave (infinite)

Quizplus · Accepted Answer

According to Heisenberg's Uncertainty Principle, the product of the uncertainty in position and momentum of a particle is equal to or greater than Planck's constant divided by 2π. Mathematically, ∆x ∆p ≥ h/2π. As the length of the wave packet representing the particle gets shorter, the uncertainty in position (∆x) increases, and therefore the uncertainty in momentum (∆p) also increases to satisfy the inequality. Option A has the smallest length among the given options, indicating the largest uncertainty in velocity, and thus it is the correct choice.

Because of Heisenberg's Uncertainty Principle,the Velocity of a Particle Is