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Q.

If $Δ x$ is the uncertainity in position and $Δ ϑ$ is the uncertainity in velocity of a particle are equal, the correct expression for uncertainity in momentum for the same particle is

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a

$\frac{1}{2} \sqrt{\frac{h}{m π}}$

b

$\frac{1}{3} \sqrt{\frac{m h}{2 π}}$

c

$\frac{1}{4} \sqrt{\frac{m h}{π}}$

d

$\frac{1}{2} \sqrt{\frac{m h}{π}}$

answer is C.

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Detailed Solution

Given condition, $Δ x = Δ v$
$Δ p . Δ x = \frac{h}{4 π}$
Or, $m Δ v . Δ v = \frac{h}{4 π}$
Or $Δ v = \sqrt{\frac{h}{4 π m}} = \frac{1}{2} \sqrt{\frac{h}{π m}}$
$∴$ Uncertainty in momentum,
$Δ p = m Δ v = \frac{m}{2} \sqrt{\frac{h}{π m}} = \frac{1}{2} \sqrt{\frac{h m}{π}}$

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