Question

The position of a baseball of 0.145 kg is measured with an accuracy of 0.0100 mm. 1. What is the uncertainty in the speed of the ball? 2. If it were a proton in an atom, whose charge is 1.6 * 10^{-19}C and its mass is 1.67 * 10^{-27}kg, what is the uncertainty in the velocity of the proton?

Answer #1

1) using the heisenberg uncertainty principle we have

p * x = h/4pi

mv *x = h/4pi

0.145*v*0.01*10^-3 = 6.626*10^-34 / 4pi

v = 3.64*10^-29 m/s

2) 1.67*10^-27*v*0.01*10^-3 = 6.626*10^-34 / 4pi

v = 0.003 m /s

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