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Question: Answered & Verified by Expert
If uncertainty in position and momentum are equal, then uncertainty in velocity is
ChemistryStructure of AtomNEETNEET 2008 (Mains)
Options:
  • A $\sqrt{\frac{h}{\pi}}$
  • B $\frac{1}{2 m} \sqrt{\frac{h}{\pi}}$
  • C $\sqrt{\frac{h}{2 \pi}}$
  • D $\frac{1}{m} \sqrt{\frac{h}{\pi}}$
Solution:
2489 Upvotes Verified Answer
The correct answer is: $\frac{1}{2 m} \sqrt{\frac{h}{\pi}}$
$\Delta x=\Delta p$
$$
\Delta p^2=\frac{h}{4 \pi}
$$
or $\Delta p=\frac{1}{2} \sqrt{\frac{h}{\pi}}$
or $m \Delta v=\frac{1}{2} \sqrt{\frac{h}{\pi}}$
or $\Delta v=\frac{1}{2 m} \sqrt{\frac{h}{\pi}}$

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