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

The Heisenberg Uncertainty Principle states that the more precisely the position of a particle is known, the less precisely its momentum can be known, and vice versa. The wave packet representing a particle has a certain width, which is related to the uncertainty in the particle's position. The narrower the wave packet, the more precisely the particle's position is known. However, the narrower the wave packet, the more spread out the wave packet is in momentum space, which means that the less precisely the particle's momentum is known.Therefore, the velocity of a particle is known least precisely when the length of the wave packet representing the particle is smallest. This is because the smaller the wave packet, the more precisely the particle's position is known, and the less precisely its momentum is known. The velocity of a particle is related to its momentum, so the less precisely the particle's momentum is known, the less precisely its velocity is known.

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