The half-life of a radioactive substance is $5$ years. After $x$ years,a given sample of the radioactive substance gets reduced to $6.25 \%$ of its initial value. The value of $x$ is ...............

The decay constants of a radioactive substance for $\alpha$ and $\beta$ emission are $\lambda_{\alpha}$ and $\lambda_{\beta}$ respectively. If the substance emits $\alpha$ and $\beta$ simultaneously,then the average half-life of the material will be:

The half-life of a radioactive isotope $X$ is $50$ years. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1 : 15$ in a sample of a given rock. The age of the rock was estimated to be..........$years$.

Half-lives for $\alpha$ and $\beta$ emission of a radioactive material are $16$ years and $48$ years respectively. When the material decays by giving $\alpha$ and $\beta$ emission simultaneously,the time in which $3/4$th of the material decays is ....... years.

One mole of radium has an activity of $\frac{1}{3.7} \text{ kilo curie}$. Its decay constant is (Avogadro number $= 6 \times 10^{23} \text{ mol}^{-1}$)

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: