The half-life period of radium is $1600$ years. The fraction of a sample of radium that would remain after $6400$ years is

Two radioactive materials $X_1$ and $X_2$ have decay constants $5\lambda$ and $\lambda$ respectively. Initially,they have the same number of nuclei. The ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $\frac{1}{e}$ after a time:

$A$ radioactive sample has an activity $A$ in air. If the sample is kept inside water,then its activity $A^{\prime}$

The specific activity of radium is close to:

The number of half-lives elapsed before $93.75 \%$ of a radioactive sample has decayed 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):