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.