The mean life of a radioactive material for alpha decay and beta decay are,respectively,$1620$ years and $520$ years. What is the half life of the sample (in years)?

The graph represents the decay of a newly prepared sample of radioactive nuclide $X$ to a stable nuclide $Y$. The half-life of $X$ is $\tau$. The growth curve for $Y$ intersects the decay curve for $X$ after time $T$. What is the time $T$?

The specific activity of $Ra^{226}$ is $1 \, Ci/g$. The activity of $1 \, \mu g$ of $Ra^{226}$ will be:

$A$ radioactive substance emits $100$ beta particles in the first $2 \,s$ and $50$ beta particles in the next $2 \,s$. The mean life of the sample is

The count rate of a Geiger-Muller counter for the radiation of a radioactive material with a half-life of $30\, minutes$ decreases to $5\, s^{-1}$ after $2\, hours$. The initial count rate was..........$s^{-1}$.

$A$ freshly prepared radioactive sample of half-life $1$ hour emits radiations that are $128$ times as intense as the permissible safe limit. The minimum time after which this sample can be safely used is ......... $hours$.