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Calculate the uncertainty in position of...

Calculate the uncertainty in position of an electron, if `Deltav = 0.1% and v = 2.2 xx 10^(6) ms^(-1)`.

Text Solution

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`Deltax cdot Deltap ge h/(4 pi)`
`Deltax . Deltap ge 5.28 xx 10^(-35) Kg m^(2)s^(-1)`
`Deltax.(m Deltav) ge 5.28 xx 10^(-35) Kgm^2s^(-1)`
Given `Deltav = 0.1 %`
`v = 2.2 xx 10^6 ms^(-1)`
`m = 9.1 xx 10^(-31) Kg`
`Deltav = (0.1)/(100) xx 2.2 xx 10^6 ms^(-1)`
`= 2.2 xx 10^3 ms^(-1)`
`:. Deltax ge (5.28 xx 10^(-35) Kgm^2s^(-1))/(9.1 xx 10^(-31) Kg xx 2.2 xx 10^3 ms^(-1))`
`Delta x ge 2.64 xx 10^(-8) m`.
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