Answer
See explanation.
Work Step by Step
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.
