Question

The relation between uncertainty in position and momentum is given by of a particle simultaneously decided

• A. de-Broglie
• B. Werner Heisenberg
• C. Neils Bohr
• D. Erwin Schrodinger

Hint:

To distinguish between the scientists:
- de-Broglie: Proposed the wave-particle duality (\(\lambda = h/mv\)).
- Bohr: Proposed the quantized energy levels in atoms.
- Heisenberg: Proposed the Uncertainty Principle.
- Schrodinger: Developed the wave equation for quantum mechanics.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the name of the scientist who formulated the mathematical relationship describing the inherent limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously.

Step 2: Key Formula or Approach:
The relationship is known as the Heisenberg Uncertainty Principle. It is mathematically expressed as: \[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \] Where:
- \(\Delta x\) is the uncertainty in position.
- \(\Delta p\) is the uncertainty in momentum.
- \(h\) is Planck's constant.

Step 3: Detailed Explanation:
In 1927, the German physicist Werner Heisenberg stated that it is impossible to determine simultaneously and precisely both the position and the momentum of a microscopic particle like an electron.
- If the position of an electron is known with high accuracy (\(\Delta x\) is small), then its velocity or momentum becomes very uncertain (\(\Delta p\) is large), and vice versa.
- This principle is a fundamental consequence of the wave-particle duality of matter.

Step 4: Final Answer:
The relation was given by Werner Heisenberg, which corresponds to option (B).