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An electron with kinetic energy T~~4eV is confirned within a region whose linear dimension is l=1 mu m. Using the uncertianty principle, evaluate the relative uncertainty of its velocity. |
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Answer» Solution :The momentum the electron is `Deltap_(X)=sqrt(2mT)` Uncertainty in its momentum is `DELTA p_(x)geħ//Deltax=ħ//l` Hence relative nucertainty `(Delta P_(x))/(p_(x))=(ħ)/(lsqrt(2mT))=sqrt((ħ^(2))/(2ml^(2)))//T=(Deltav)/(v)` SUBSTITUTION GIVES `(Delta v)/(v)=(Delta p)/(p)= 9.75xx10^(-5)~~10^(-4)` |
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