## University Physics with Modern Physics (14th Edition)

The Heisenberg uncertainty principle limits our knowledge. $$\Delta E \Delta t \geq \frac{\hbar}{2}$$ Find the minimum uncertainty in energy. $$\Delta E = \frac{\hbar}{2\;\Delta t}$$ $$\Delta E = 6.277\times10^{-19}J$$ Convert to a mass uncertainty. $$\Delta m = \frac{\Delta E}{c^2}=6.98\times10^{-36}kg$$ Calculate this as a fraction of the mass. $$\frac{\Delta m}{m}=\frac{6.98\times10^{-36}kg }{264m_e}=2.9\times10^{-8}$$ The uncertainty in the mass is a tiny fraction of the mass.