The uncertainty in the position of an electron $(mass = 9 .1 \times 10^{- 28} g)$ moving with a velocity of $3 .0 \times 10^{4} {cms}^{- 1}$ accurate up to 0.011% will be

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3.84 cm

7.68 cm

1.92 cm

0.175 cm

answer is C.

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Detailed Solution

$Δ x . Δ p = \frac{h}{4 π} or Δ x . m Δ v = \frac{h}{4 π} Δ v = \frac{0.011}{100} \times 3 \times 10^{4} = 3.3 {cms}^{- 1} Δ x = \frac{6.6 \times 10^{- 27}}{4 \times 3.14 \times 9.1 \times 10^{- 28} \times 3.3} = 0.175 cm$

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