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Question: Answered & Verified by Expert
If the uncertainty in momentum and uncertainty in the position of a particle are equal, then the uncertainty in its velocity would be given by
ChemistryStructure of AtomAP EAMCETAP EAMCET 2021 (24 Aug Shift 1)
Options:
  • A $\Delta v \geq \sqrt{\frac{h}{2 \pi}}$
  • B $\Delta v \geq \frac{1}{2 m} \sqrt{\frac{h}{\pi}}$
  • C $\Delta v \geq \sqrt{\frac{h}{\pi}}$
  • D $\Delta v \geq \frac{1}{m} \sqrt{\frac{h}{\pi}}$
Solution:
2884 Upvotes Verified Answer
The correct answer is: $\Delta v \geq \frac{1}{2 m} \sqrt{\frac{h}{\pi}}$
$\begin{aligned} \text { } \Delta P=\Delta x & \text { (Given) } \\ \Delta x \cdot \Delta P \geq \frac{h}{4 \pi} & \text { (Uncertainty principle) } \\ \Delta P^2 & \geq \frac{h}{4 \pi} \\ (m \times \Delta v)^2 & \geq \frac{h}{4 \pi} \\ \Delta v & \geq \frac{1}{2 m} \sqrt{\frac{h}{\pi}} .\end{aligned}$

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