The size of a microscopic particle is one micron and its mass is $6 \times 10^{- 13}$ gm. If its position may be measured to within 0.1% of its size, the uncertainty in velocity, in cm $S^{- 1}$ , is approximately

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$10^{- 6} / 3 π$

$10^{- 7} / 2 π$

$10^{- 5} / 4 π$

$10^{- 7} / 4 π$

answer is D.

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Detailed Solution

$Δ p . Δ x = h / 2 π$

$m . Δ v . Δ x = h / 2 π$

$Δ v = \frac{1}{4 π} \times \frac{h}{m . Δ x}$

$m = 6 \times 10^{- 13} g$

$Δ x = \frac{0.1}{100} \times 10^{- 4} c m = 10^{- 7} c m$

$Δ v = \frac{1}{4 π} \times \frac{6.626 \times 10^{27}}{6 \times 10^{13} \times 10^{7}} c m s^{- 1}$

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