Problem 6.217

To investigate the beta-decay of $\mathrm{Mg}^{23}$ radionuclide, a counter was activated at the moment $t=0$. It registered $N_{1}$ beta-particles by a moment $t_{1}=2.0 \mathrm{~s}$, and by a moment $t_{2}=3 t_{1}$ the number of registered beta-particles was 2.66 times greater. Find the mean lifetime of the given nuclei.