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Q.

The mass of a particle is 10^-10 g and its radius is 2 x 10^-4 cm. If its velocity is 10^-6 cm sec^-1 with 0.0001% uncertainty in measurement, the uncertainty in its position is :

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a

5.2 x 10^-8 m

b

5.2 x 10^-7 m

c

5.2 x 10^-6 m

d

5.2 x 10^-9 m

answer is A.

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Detailed Solution

$m = 10^{- 10} g \Rightarrow 10^{- 13} kg \begin{array}{l} Δv = \frac{0 .0001}{100} \times 10^{- 6} \times 10^{- 2} = 10^{- 14} m \sec^{- 1} \\ = Δx \cdot Δp = \frac{h}{4 π} \\ \Rightarrow Δx = \frac{h}{4 πΔp} = \frac{h}{4 π \cdot mΔv} \\ Δx = \frac{6 .62 \times 10^{- 34}}{4 \times 3 .14 \times 10^{- 13} \times 10^{- 14}} \\ Δx = \frac{6 .62}{12 .56} \times \frac{10^{- 34}}{10^{- 27}}; Δx = 5 .2 \times 10^{- 8} m \end{array}$

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The mass of a particle is 10-10 g and its radius is 2 x 10-4 cm. If its velocity is 10-6 cm sec-1 with 0.0001% uncertainty in measurement, the uncertainty in its position is :