The decay constant of a radioactive element is $1.5 \times 10^{-9} \text{ s}^{-1}$. Its mean life in seconds will be:

The half-life of radium is $1600 \, \text{years}$. After how many years will $25 \, \text{g}$ of radium remain from $100 \, \text{g}$ of radium?

$A$ radioactive sample decays $\frac{7}{8}$ times its original quantity in $15$ minutes. The half-life of the sample is $......$ minutes.

The half-lives of a radioactive substance are $T$ and $2T$ years for $\alpha$-emission and $\beta$-emission,respectively. The total decay constant for the simultaneous decay of the $\alpha$ and $\beta$ radioactive substance is:

Two different radioactive elements with half-lives $T_1$ and $T_2$ have undecayed atoms $N_1$ and $N_2$ respectively present at a given instant. The ratio of their activities at that instant is

The half-life of a radioactive element is $30$ days. What percentage of the element will have decayed in $90$ days?