### Correct Option: B **Explanation of the Heisenberg Uncertainty Principle:** The Heisenberg Uncertainty Principle is a fundamental concept in quantum mechanics that describes a limit to the precision with which certain pairs of physical properties, known as complementary variables or canonically conjugate variables, can be known simultaneously. The most commonly discussed pair of these variables are position (x) and momentum (p). 1. **Understanding Position and Momentum:** - **Position (x)** refers to the location of a particle in space. - **Momentum (p)** is defined as the product of a particle's mass (m) and its velocity (v), expressed mathematically as \( p = mv \). 2. **The Principle Statement:** - The Heisenberg Uncertainty Principle states that the more precisely we know a particle's position (Δx), the less precisely we can know its momentum (Δp), and vice versa. This relationship can be mathematically expressed as: \[ Δx \cdot Δp \geq \frac{\hbar}{2} \] where \( \hbar \) (h-bar) is the reduced Planck's constant, approximately \( 1.055 \times 10^{-34} \, \text{Js} \). 3. **Implications of the Principle:** - This principle implies that there is a fundamental limit to measurement in quantum mechanics. It is not just a limitation of our measuring instruments but a reflection of the intrinsic nature of quantum systems. When we try to measure the position of a particle very accurately, the uncertainty in its momentum increases, and vice versa. 4. **Why Option B is Correct:** - Option B accurately captures the essence of the Heisenberg Uncertainty Principle. It states that there is a trade-off between the precision of measuring position and momentum. This is a core concept in quantum mechanics and highlights the non-deterministic nature of quantum particles. ### Why the Other Options are Incorrect: - **Option A: "Both position and momentum can be known with absolute precision simultaneously."** - This option is incorrect because it directly contradicts the Heisenberg Uncertainty Principle. The principle asserts that it is impossible to know both properties with absolute precision at the same time. This is a fundamental aspect of quantum mechanics. - **Option C: "The uncertainty in position is always greater than the uncertainty in momentum."** - This statement is misleading. The Heisenberg Uncertainty Principle does not state that the uncertainty in position (Δx) is always greater than the uncertainty in momentum (Δp). Instead, it establishes a relationship between the two uncertainties, indicating that their product is bounded by a constant. Depending on the system, either uncertainty could be greater. - **Option D: "Particles do not have defined positions or momenta until they are measured."** - While this statement touches on the concept of wave function collapse in quantum mechanics, it is not a direct statement of the Heisenberg Uncertainty Principle. The principle does not claim that particles lack defined properties; rather, it states that there is a limit to how precisely we can know those properties simultaneously. ### Summary of Key Points: - The Heisenberg Uncertainty Principle states that the more accurately we know a particle's position, the less accurately we can know its momentum, and vice versa. - This principle is mathematically expressed as \( Δx \cdot Δp \geq \frac{\hbar}{2} \). - It reflects a fundamental limit in quantum mechanics, not just a limitation of measurement tools. - Understanding this principle is crucial for grasping the non-deterministic nature of quantum systems.