According to the Heisenberg uncertainty principle, quantum mechanics differs from classical mechanics in that: Select the correct answer below: Quantum mechanics involves particles that do not move. It is impossible to calculate with accuracy both the position and momentum of particles in classical mechanics. The measurement of an observable quantity in the quantum domain inherently changes the value of that quantity. All of the above

Statement 3 is correct.

Heisenberg's uncertainty principle explains that the measurement of an observable quantity in the quantum domain inherently changes the value of that quantity

Explanation:

Classical mechanics is the study of motion of big, relatable bodies that we come in contact with in our day to day lives.

Quantum mechanics refers to this same study, but for particles on a subatomic level.

Obviously, Classical mechanics' theories and principles were first discovered and they worked for their intended uses (still work!). But when studies on particles on a sub-atomic level intensified, it became impractical to apply those theories and principles to these sub-atomic particles that displayed wave-particle duality nature properly.

Heisenberg's Uncertainty principle came in a time that explanations and justifications were needed to adapt these theories to sub-atomic particles.

The principle explains properly that it is impossible to measure the position and velocity (momentum) of a sub-atomic particle in exact terms and at the same time.

Mathematically, it is presented as

Δx.Δp ≥ ℏ

Where ℏ= adjusted Planck's constant.

ℏ= (h/2π)

And Δx and Δp are the uncertainties in measuring the position and momentum of sub-atomic particles.

The major reason for this is the wave-particle duality of sub-atomic particles. They exist as waves and particles at the same time that a complete knowledge of their position mean that a complete ignorance of their velocity and vice versa.

Taking the statements one at a time

Statement 1

Quantum Mechanics studies sub-atomic particles which are mostly always in motion. So, this is false.

Statement 2

It is impossible to calculate with accuracy both the position and momentum of particles in quantum mechanics not classical mechanics. As stated above, the reason for the uncertainty is the wave-particle duality of sub-atomic particles which the particle in classical mechanics do not exhibit obviously enough.

Statement 3

Any attempt to measure precisely the velocity of a subatomic particle, will knock it about in an unpredictable way, so that a simultaneous measurement of its position has no validity.

An essential feature of quantum mechanics is that it is generally impossible, even in principle, to measure a system without disturbing it. This is basically the uncertainty principle rephrased. This is the only true statement.

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