Question

According to the Heisenberg's Uncertainty principle, the value of \(\Delta v \cdot \Delta x\) for an object whose mass is \(10^{-6}\) kg is

• A. \(4.0 \times 10^{-26} \, \text{ms}^{-1}\)
• B. \(3.5 \times 10^{-25} \, \text{ms}^{-1}\)
• C. \(5.2 \times 10^{-29} \, \text{ms}^{-1}\)
• D. \(3.0 \times 10^{-24} \, \text{ms}^{-1}\)

Hint:

Heisenberg's Uncertainty principle provides a relationship between the uncertainty in position and momentum, and it can be applied to calculate uncertainties in velocity and position.

Answer 1

The Correct Option is C

According to Heisenberg's Uncertainty principle: \[ \Delta v \cdot \Delta x \geq \frac{h}{4\pi m} \] Where: - \(h = 6.626 \times 10^{-34} \, \text{Js}\) (Planck's constant) - \(m = 10^{-6} \, \text{kg}\) (mass of the object) Now, substitute the given values: \[ \Delta v \cdot \Delta x = \frac{6.626 \times 10^{-34}}{4 \pi \times 10^{-6}} = 5.2 \times 10^{-29} \, \text{ms}^{-1} \] Thus, the correct answer is Option (3).