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Chemistry · Structure of atom
हिन्दीA microscopic particle of mass \( 10^{-6} \text{ kg} \) has an uncertainty in position of \( 10^{-6} \text{ m} \). The minimum percentage uncertainty in its velocity is approximately equal to:
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Correct answer · Option D
\( 5.27 \times 10^{-24}\% \)
Explanation
From \( \Delta v \cdot \Delta x \ge \frac{h}{4\pi m} \), \( \Delta v = \frac{6.626 \times 10^{-34}}{4 \times 3.1416 \times 10^{-6} \times 10^{-6}} \approx 5.27 \times 10^{-23} \text{ m s}^{-1} \). Assuming reference speed of \( 1 \text{ m s}^{-1} \), the percentage uncertainty evaluates to \( 5.27 \times 10^{-21}\% \).
