QJEEM22Ch277a: JEE Main 2022 Chemistry - Class 11 JEEM22Ch277a Solution: The minimum uncertainty in the speed of an electron in an one…

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QJEEM22Ch277a: JEE Main 2022 Chemistry - Class 11 JEEM22Ch277a Solution: The minimum uncertainty in the speed of an electron in an one…

The minimum uncertainty in the speed of an electron in an one dimensional region of length $2 a_{o}$ (Where $a_{o} =$ Bohr radius $52.9 pm$ ) is _________ $km s^{- 1}$ .

(Given : Mass of electron = 9.1 $\times$ 10^{$-$ 31} kg, Planck's constant h = 6.63 $\times$ 10^{$-$ 34} Js)

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Accepted Answer

Heisenberg's uncertainty principle

\begin{aligned} Δ x \times Δ P_{x} \geq \frac{h}{4 π} \\ \Rightarrow 2 a_{0} \times m Δ v_{x} = \frac{h}{4 π} (minimum) \\ \Rightarrow Δ v_{x} = \frac{h}{4 π} \times \frac{1}{2 a_{0}} \times \frac{1}{m} \\ = 6.63 \times 10^{- 34} \end{aligned}

\begin{aligned} 4 \times 3.14 \times 2 \times 52.9 \times 10^{- 12} \times 9.1 \times 10^{- 31} \\ = 548273 {ms}^{- 1} \\ = 548.273 {kms}^{- 1} \\ = 548 {kms}^{- 1} \end{aligned}

QJEEM22Ch277a: JEE Main 2022 Chemistry - Class 11 JEEM22Ch277a Solution: The minimum uncertainty in the speed of an electron in an one…

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