An element used for radioactive carbon dating for more than $5600$ years is

The half-life of a radioactive nucleus is $50$ days. The time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it had decayed and the time $t_1$ when $\frac{1}{3}$ of it had decayed is (in days):

The half-life of a radioactive substance is $12 \text{ minutes}$. The time gap between $28 \%$ decay and $82 \%$ decay of the radioactive substance is

The activities of three radioactive substances $A, B$ and $C$ are represented by the curves $A, B$ and $C$ in the figure. Then their half-lives $T_{\frac{1}{2}}(A) : T_{\frac{1}{2}}(B) : T_{\frac{1}{2}}(C)$ are in the ratio:

The phenomenon of radioactivity is

The radioactivity of a certain radioactive element drops to $\frac{1}{64}$ of its initial value in $30$ seconds. Its half-life is ............. seconds.