A particle of mass one microgram is confined to move along one direction (x-axis) within a region 1 mm in extension. What is the uncertanity in its velocity (cm/sec)?

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5.27 × 10^–21

5.012 × 10^–20

3.313 × 10^–20

8.325 × 10^–20

answer is D.

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Detailed Solution

m=1μg =10⁻⁶ g=10⁻⁹ kg.
Δx=1mm=10 ⁻³ m

$∆ x . m . ∆ v \geq \frac{h}{4 π} ∆ v \geq \frac{h}{4 π ∆ x . m} ∆ v \geq \frac{6.628 \times 10^{- 34}}{4 \times 3.14 \times 10^{- 9 \times 10^{- 3}}} = 5.27 \times 10^{- 21} cm / \sec$

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