If uncertainties in the measurement of position and momentum of a microscopic object of mass ‘m’ are equal, then the uncertainity in the measurement of velocity is given by the expression

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$\frac{h}{4 π} \times \sqrt{\frac{1}{m}}$

$\sqrt{\frac{h}{2 πm}}$

$\sqrt{\frac{h}{4 π}} \times \frac{1}{m}$

$\sqrt{\frac{h}{4 πm}}$

answer is B.

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Detailed Solution

$∆ x . ∆ p = \frac{h}{4 π} G i v e n, ∆ x = ∆ p ∆ p . ∆ p = \frac{h}{4 π} ∆ p^{2} = \frac{h}{4 π} ∆ p^{} = \sqrt{\frac{h}{4 π}} m . ∆ v = \sqrt{\frac{h}{4 π}} ∆ v = \frac{1}{m} \sqrt{\frac{h}{4 π}} o r \frac{1}{2 m} \sqrt{\frac{h}{π}}$

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