Estimate the minimum errors in determining the velocity of an electron, a proton, and a ball of mass of 1 mg if the coordinates of the particles and of the centre of the ball are known with uncertainly 1 mu m.

Estimate the minimum errors in determining the velocity of an electron

1.	Estimate the minimum errors in determining the velocity of an electron, a proton, and a ball of mass of 1 mg if the coordinates of the particles and of the centre of the ball are known with uncertainly 1 mu m.
Answer» Solution :From the uncertainty principle (Eqn.(6.2b)) `DeltaxDelataP_(x)underset(~) gt ħ` THUS `Deltap_(x)=mDeltav_(x)underset(~) gt ( ħ)/(Deltax)` or `Deltav_(x)underset(~) gt ( ħ)/(mDelta_(x))` For an electron this means an uncertiainty in velocity of `116mm//s` if `Deltax=10^(-6)m=1 mu m` For a proton For a BALL `Deltav_(x)=1xx10^(-20)cm//s`

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Estimate the minimum errors in determining the velocity of an electron, a proton, and a ball of mass of 1 mg if the coordinates of the particles and of the centre of the ball are known with uncertainly 1 mu m.

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