The mass of a praticle is 10^–10g and its radius is 2 × 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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5.2 × 10^–8m

5.2 × 10^–7m

5.2 × 10^–6m

5.2 × 10^–9m

answer is A.

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Detailed Solution

$\begin{array}{l} mass = 10^{- 10} g = 10^{- 13} kg \\ ΔV = 0 .0001 % of V \\ = \frac{0 .0001}{100} \times 10^{- 6} = 10^{- 14} m / s \\ Δx \times ΔV = \frac{h}{4 λm} \\ Δx = 5 .2 \times 10^{- 8} \end{array}$

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