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The isotopes $Ra-226$ undergoes $\alpha$ decay with a half-life of $1620$ years. What is the activity of $1\;g$ of $Ra-226$? Avogadro number = $6.023 * 10^{23}\; /mole$.

Find the half-life of $U^{238}$, if one gram of it emits $1.24 * 10^4$ $\alpha - particles$ per second. (Avogadro's Number = $6.023 * 10^{23}$).