Heisenberg's uncertainty principle can be expressed by

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  1. \(\Delta x \times \Delta p \ge \frac{h}{\pi}\)
  2. \(\Delta p \ge \frac{h}{\Delta x}\)
  3. \(\Delta x \times \Delta p \ge \frac{h}{4\pi}\)
  4. \(\Delta x \times \Delta p \ge \frac{h}{2\pi}\)

Answer (Detailed Solution Below)

Option 3 : \(\Delta x \times \Delta p \ge \frac{h}{4\pi}\)
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EXPLANATION:

Heisenberg's Uncertainty Principle

  • The Heisenberg Uncertainty Principle is a fundamental concept in quantum mechanics.
  • It states that it is impossible to simultaneously determine the exact position (Δx) and momentum (Δp) of a particle with absolute precision.
  • The principle is mathematically expressed as:

    Δx × Δp ≥ h / (4π)

    where:
    • Δx = uncertainty in position
    • Δp = uncertainty in momentum
    • h = Planck’s constant
  • Among the given options:
    • Option (3): Δx × Δp ≥ h / 4π is the correct standard form of the Heisenberg uncertainty relation.

Therefore, the correct answer is Δx × Δp ≥ h / 4π

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