 JEE Mains Previous Years Questions with Solutions

4.5
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1

AIEEE 2002

Uncertainty in position of a minute particle of mass 25 g in space is 10-5 m. What is the uncertainty in its velocity (in ms-1) (h = 6.6 $\times$ 10-34 Js)
A
2.4 $\times$ 10-34
B
0.5 $\times$ 10-34
C
2.1 $\times$ 10-28
D
0.5 $\times$ 10-23

Explanation

According to Hysenberg's Uncertainty Principal $$\Delta x . \Delta p \ge { h \over {4\pi}}$$ Where $\Delta x$ is uncertainty in position and $\Delta p$ is uncertainty in momentum and as in momentum m (mass of object) is always same so we can say $$\Delta x . m. \Delta v \ge { h \over {4\pi}}$$ Mass of the particle (m) = 25 g = 0.025 kg

Position of the particle ($\Delta x$) = 10-5 m

$\Delta x . \Delta p$ = ${ h \over {4\pi}}$

$\Delta x . m . \Delta v$ = ${ h \over {4\pi}}$

$\Delta v$ = ${h \over {4 \times \Delta x \times m \times \pi }}$

$\Delta v$ = ${{6.6 \times {{10}^{ - 34}}} \over {4 \times {{10}^{ - 5}} \times 0.025 \times 3.14}}$

$\Delta v$ = 2.1 $\times$ 10-28