Question

A golf ball has a mass of 40 g, and a speed of 45 m/s. If the speed can be measured with in accuracy of 2%. Calculate the uncertainty in the position.

Answer 1

The uncertainty in the speed is 2% i.e.

45 x \(\frac{2}{100}\) = 0.9 m/s

According to Heisenberg uncertainty,

∆x × m∆v = \(\frac{h}{4\pi}\)

\(\therefore\) ∆x = \(\frac{h}{4\pi m\Delta v}\)

= \(\frac{6.626\times10^{-34}Js}{4\times3.14\times40\times10^{-3}kg\times0.9m/s}\)

=1.46 × 10⁻³³ m

This is nearly ~10¹⁸ times smaller than the diameter of a typical atomic nucleus.