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If uncertainty in the measurement of position and momentum are equal, then uncertainty in the measurement of velocity is equal to:
$\frac{1}{2 m} \sqrt{\frac{2 h}{π}}$
$\frac{1}{2 m} \sqrt{\frac{h}{π}}$
$\frac{1}{4 m} \sqrt{\frac{h}{π}}$
$\frac{1}{2 m} \sqrt{\frac{h}{2 π}}$

A

\frac{1}{4 m} \sqrt{\frac{h}{π}}

B

\frac{1}{2 m} \sqrt{\frac{2 h}{π}}

C

\frac{1}{2 m} \sqrt{\frac{h}{π}}

D

\frac{1}{2 m} \sqrt{\frac{h}{2 π}}

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Solution

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If uncertainty in the measurement of position and momentum are equal then uncertainly in the measurement of velocity is equal to $\frac{1}{2 m} \sqrt{\frac{h}{π}}$ .
$Δ x Δ P = \frac{h}{4 π}$
But $Δ x = Δ P$
Hence, $Δ x = Δ P = \sqrt{\frac{h}{4 π}}$
But $Δ P = m Δ u$
Hence,
$Δ u = \frac{1}{2 m} \sqrt{\frac{h}{π}}$

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