Problem 12: The speed of an electron is measured to be 5 × 103 m/s to an accuracy of 0.003%. Find the uncertainty in determining the position of this electron.

Solution

Given: Speed of electron, v = 5 × 10^{-3} m/s Accuracy limit . 0.003 %

Find: Uncertainty in position, Δx

Accuracy in the velocity for 100 m/s = 0.003 m/s

Accuracy for total velocity is

Now, the uncertainty principle says, the product of uncertainty in momentum (mv) and its position Δx at some instant is approximately equal to Planck’s constant, h. Therefore, Δ(mv)Δx = h … (A)

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