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A golf ball of mass 40 g moves with a speed of 45 m/s. If the speed is measured to an accuracy of 2%, what is the minimum uncertainty in its position (using Heisenberg's uncertainty principle)?
- About 1.5 * 10⁻³³ m
- About 1.5 * 10⁻³¹ m
- About 3.0 * 10⁻³⁰ m
- About 9.1 * 10⁻³⁵ m
Correct answer: About 1.5 * 10⁻³³ m
Solution
The velocity uncertainty is 2% of 45 = 0.9 m/s, so dp = 0.04*0.9 = 0.036 kg m/s; then dx = h/(4*pi*dp) gives about 1.5 * 10⁻³³ m.
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