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If uncertainties in the measurement of p...

If uncertainties in the measurement of position and momentum of an electron are found to be equal in magnitude, then what is the uncertainty in the measurement of velocity? Comment on the result.

Text Solution

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According to uncertainty principle, `Deltax xxDeltap=(h)/(2pi)`
given, `Deltax=Deltap`
`therefore (Deltap)^(2)=(h)/(2pi), or, Deltap=sqrt((h)/(4pi))`
or, `mDeltav=sqrt((h)/(4pi)), or Deltav=(1)/(m)sqrt((h)/(4pi))`
`=(1)/(9.11xx10^(-31))sqrt((6.626xx10^(-34))/(4xx3.14))=7.97xx10^(12)xx10^(12)m*s^(-1)`
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