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Q.

Mass of a particle is $5.27 \times 10^{- 21} Kg .$ It is moving with a velocity of $10^{5} m / s .$ If the uncertainty in measuring its velocity is $0.01 %$ then the uncertainity in measuring its position will be……meters

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a

$10^{- 21}$

b

$10^{- 22}$

c

$10^{- 12}$

d

$10^{- 15}$

answer is C.

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Detailed Solution

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$∆ x = \frac{h}{4 πm} \times \frac{1}{∆ v}; Given, v = 10^{5} m / s; ∆ v = 10^{5} \times \frac{0.01}{100} m / s; ∆ v = 10 m / s; Given, m = 5.27 \times 10^{- 21} Kg; ∆ x = \frac{6.625 \times 10^{- 34} J . s}{4 \times 3.14 \times 5.27 \times 10^{- 21} Kg} \times \frac{1}{10 m / s}; ∆ x = 10^{- 15} m;$

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