A dust particle of mass 10^–11g is moving with a velocity of 10^–4cm/s. If error in calculating the velocity is 0.1% what will be the uncertinity in its position

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$5.29 \times 10^{- 10} m$

$5.29 \times 10^{- 9} m$

$5.29 \times 10^{- 10} cm$

None

answer is B.

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Detailed Solution

$m = 10^{- 11} g, ∆ V = 10^{- 4} \times \frac{0.1}{100} cm / s . = 10^{- 7} cm / s . ∆ x = \frac{h}{4 πm ∆ V} = \frac{6.625 \times 10^{- 27}}{4 \times 3.14 \times 10^{- 11} \times 10^{- 7}} = 5.29 \times 10^{- 10} cm$

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