QJEEM22Ch76fe: JEE Main 2022 Chemistry - Class 11 JEEM22Ch76fe Solution: If the uncertainty in velocity and position of a minute…

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QJEEM22Ch76fe: JEE Main 2022 Chemistry - Class 11 JEEM22Ch76fe Solution: If the uncertainty in velocity and position of a minute…

If the uncertainty in velocity and position of a minute particle in space are, 2.4 $\times$ 10^{$-$ 26} (m s^{$-$ 1}) and 10^{$-$ 7} (m) respectively. The mass of the particle in g is ____________. (Nearest integer)

(Given : h = 6.626 $\times$ 10^{$-$ 34} Js)

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Accepted Answer

We know from hisenberg uncertainty principle

$Δ x . Δ p = \frac{h}{4 π}$

$\Rightarrow Δ x . m Δ v = \frac{h}{4 π}$

Given,

$Δ$ x = 10^{$-$ 7} m

$Δ$ x = 2.4 $\times$ 10^{$-$ 26} m/s

h = 6.626 $\times$ 10^{$-$ 34} Js

$∴$ $10^{- 7} \times m \times 2.4 \times 10^{- 26} = \frac{6.626 \times 10^{- 34}}{4 π}$

$\Rightarrow 2.4 m = \frac{6.626}{4 π \times 10}$

$\Rightarrow$ m = 0.022 kg

$\Rightarrow$ m = 22 gm

QJEEM22Ch76fe: JEE Main 2022 Chemistry - Class 11 JEEM22Ch76fe Solution: If the uncertainty in velocity and position of a minute…

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