Final answer:
The Heisenberg uncertainty principle, key to quantum mechanics, sets a limit to the precision of simultaneously determining a particle's position and momentum, significant only at the atomic level. The correct option is A.
Step-by-step explanation:
The Heisenberg uncertainty principle is one of the cornerstones of quantum mechanics. In 1929, physicist Werner Heisenberg formulated the principle, which states that precise, simultaneous measurement of both the momentum and the position of a particle is fundamentally impossible. According to this principle, the more accurately one measures a particle's position, the less accurately the momentum can be known, and vice versa.
This principle is especially significant when dealing with subatomic particles. For example, if you're trying to determine an electron's position and momentum, there's a limit to the precision with which these measurements can be made. The uncertainty, or imprecision, in measuring the position (Δx) times the uncertainty in measuring the momentum (Δpx) will always be greater than or equal to ħ/2. The value ħ represents the reduced Planck's constant (ħ = h/2π).
It's important to understand that the Heisenberg uncertainty principle does not apply to macroscopic everyday objects, but it fundamentally limits our knowledge about the behavior of particles at the atomic level. The quantum behavior of particles, like electrons, means that there's always an inherent degree of uncertainty in our measurements—no matter how sophisticated our technology gets.
Option a) from the question is the correct answer: It states that position and momentum (velocity if the mass is known) cannot be simultaneously measured with exact precision. The other options are incorrect as the principle is closely linked to quantum mechanics and does not limit us to macroscopic observations, nor does it define exact positions and velocities, and it is highly applicable to quantum mechanics.