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Uncertainty in the position of an electron (mass = 9.1 × 10^–31 kg) moving with a velocity 300ms^–1 accurate upto 0.001% will be (h = 6.63 × 10^–34Js)

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3.84 × 10^–2 m

19.2 × 10^–2m

5.76 × 10^–2 m

1.92 × 10^–2 m

answer is D.

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Detailed Solution

Δx . Δv = h/4πm;
Δv = 300 × 0.001/100
= 3 × 10^-3 m/s

$\large \Delta x = \frac{h}{{4\pi m}} \times \frac{1}{{\Delta v}}\$

$\large \ = \frac{{6.625 \times 1{0^{ - 34}}}}{{4 \times 3.14 \times 9.1 \times 1{0^{ - 31}}}} \times \frac{1}{{3 \times {{10}^{ - 3}}}} = 1.92 \times 1{0^{ - 2}}m\$

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