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  • The minimum uncertainty in the speed of an electron in an one dimensional region of length <img alt="\mathrm{2 \mathrm{a}_{\mathrm{o}}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmath

The minimum uncertainty in the speed of an electron in an one dimensional region of length \mathrm{2 \mathrm{a}_{\mathrm{o}}} \mathrm{(Where\: \mathrm{a}_{\mathrm{o}}= Bohr \: radius \left.52.9\: \mathrm{pm}\right)} is _____________ \mathrm{\mathrm{km}\: \: \mathrm{s}^{-1}}.

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

Option: 1

548


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

We know , Heisenberg's uncertainty Principle 

\mathrm{\Delta x\times \Delta v\geq \frac{h}{4\pi m}}
For the minimum uncertainty in the speed.
\mathrm{\Delta v= \frac{h}{4\pi m\times \Delta x}}

given , \mathrm{\Delta x= 2a_{0}= 2\times 52.9= 105.8\, pm}
and  \mathrm{h= 6.63\times 10^{-34}\, Js}

\mathrm{\Delta v= \frac{6.63\times 10^{-34}}{4\times 3.14\times 9.1\times 10^{-31}\times 105.8\times 10^{-12}}}
\mathrm{\Delta v= \548\: km\: s^{-1}}

Ans = 548

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