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Question

According to Heisenberg's uncertainty principle, the product of uncertainties in position and velocities for an electron of mass 9.1 × 10−31 kg is

A

2.8 × 103 m2 s1

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B

3.8 × 105 m2 s1

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C

5.8 × 105 m2 s1

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D

6.8 × 106 m2 s1

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Solution

The correct option is C 5.8 × 10−5 m2 s−1 We know ,from Heisenberg Uncertainty Principle, △x × △p = h4π ⇒ △x × △v = h4πm Given that mass of electron = 9.1 × 10−31 kg Plank's constant = 6.63 × 10−34 kg m2 s−1 By using △x × △v = h4π×m ; Where: △ x = uncertainty in position △ v = uncertainty in velocity △x × △v = h4πm = 6.63×10−344×3.14×9.1×10−31 = 5.8 × 10−5 m2 s−1

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