Question

Which of the following can be concluded from the Heisenberg Uncertainty Principle?

`A)` All things, to some extent, have both wave and particle characteristics.
`B)` The kinetic energy of a photoelectron ejected from a metal changes with frequency, and not light intensity.
`C)` Position and momentum can be measured simultaneously.
`D)` The more accurately we know the position of a particle, the less accurately we can know the velocity of that particle.

Answer 1

It is `D`, "the more accurately we know the position of a particle, the less accurately we can know the velocity of that particle". Although the wording of `D` is off; it should be about precision, not accuracy.

(Obviously, a quick google search disproves `C`, which is the exact opposite of the correct statement given by the "principle of complementarity".)

---

The Heisenberg Uncertainty Principle states that for quantum particles (such as electrons and protons),

`DeltaxDeltap >= ℏ/2`,

where `ℏ = h/(2pi)` is the reduced Planck's constant, `x` is position and `Deltap` is the uncertainty in the momentum. Recall that `p = mv`, and `v` is the velocity.

When the uncertainty in the position is low, `Deltax` is low. In order to maintain the inequality, i.e. that `DeltaxDeltap >= ℏ/2`, we must have a non-low uncertainty in the momentum.

That is, if we are sure about the position, we are less sure about the momentum and vice versa. Similarly, when we know the position more PRECISELY, we know the momentum (and thus the velocity) less PRECISELY.

We can be as accurate as we want, but precision is what the Heisenberg uncertainty principle is concerned with.