Question

Which of the following is a correct relation according to Heisenberg's Uncertainty principle? 
1. \({\rm{\Delta }}x \times {\rm{\Delta }}P\; \le \frac{h}{{4\;\pi \;}}\)
2. \({\rm{\Delta }}x \times {\rm{\Delta }}v\; \le \frac{h}{{4\;\pi \;}}\)
3. \({\rm{\Delta }}x \times {\rm{\Delta }}P\; \ge \frac{h}{{4\;\pi \;}}\)
4. \({\rm{\Delta }}x \times {\rm{\Delta }}v\; \ge \frac{h}{{4\;\pi \;}}\)

Answer 1

Correct Answer - Option 3 : \({\rm{\Delta }}x \times {\rm{\Delta }}P\; \ge \frac{h}{{4\;\pi \;}}\)

Concept:

Heisenberg’s Uncertainty Principle:

• W Heisenberg a German physicist in 1927, stated the uncertainty principle which is the consequence of dual behavior of matter and radiation.
• It states that it is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron.

Explanation:

According to Heisenberg’s Uncertainty Principle

\({\rm{\Delta }}x \times {\rm{\Delta }}P\; \ge \frac{h}{{4\;\pi \;}}\)

Where, Δx = Uncertainty in position, ΔP = Uncertainty in momentum, h = Plank’s constant