A dust particle has mass equal to $10^{- 11}$ g, diameter $10^{- 4}$ cm and velocity $10^{- 4}$ cm $s^{- 1}$ . The error in measurements of velocity is 0.1%. What will be the uncertainty in its position?

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$0.527 \times 10^{- 10} m$

$5.27 \times 10^{- 9} c m$

$0.527 \times 10^{- 9} m$

$0.527 \times 10^{- 15} c m$

answer is D.

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Detailed Solution

$v = 10^{- 4} c m^{- 1} s^{- 1}$

$∴ Δ v = \frac{0.1 \times 10^{- 4}}{100} 1 \times 10^{- 7} c m s^{- 1}$

Now, $Δ v . Δ x = \frac{h}{4 π m}$

$∴ Δ x = \frac{6.626 \times 10^{- 27}}{4 \times 3.14 \times 10^{- 11} \times 10^{- 7}}$

$= 0.527 \times 10^{- 9} c m$

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