An electron moves in a straight line with a constant speed of V = 1.10 X Ten restu 6 M/s which has been measured to a precision of 0.10 percent what is the maximum precision with which its postion could be simultaneously measured?

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Atul Chhotray Profile
Atul Chhotray answered
We will have ti use the Heisenberg's uncertainty principle in this problem. So we have

Dp. Dx >= h/4*pi

where Dx denotes uncertainty in position and Dp the uncertainty in momentum.

=> Dx >= h / (4 * pi * m* Dv)
where Dv is the uncertainty in velocity.

Dv = (0.10/100) * 1.10 * 10^6 = 1.10 * 10^3 m/s [10^6 means 10 raised to the power 6]

So
Dx >=h / (4 * pi * m* 1.10 * 10^3) = 5.268 * 10^(-8) m

So the min uncertainty in position is is given by Dx which implies maximum precision.

So Dx = 5.268 * 10^(-8) m.

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