The half-life of radioactive Polonium $(Po)$ is $138.6$ days. For $10^6$ Polonium atoms,the number of disintegrations in $24$ hours is:

Radioactive material $A$ has decay constant $8 \lambda$ and material $B$ has decay constant $\lambda$. Initially,they have the same number of nuclei. After what time will the ratio of the number of nuclei of material $B$ to that of $A$ be $\frac{1}{e}$?

Half-life of a radioactive sample is $24 \,h$. If a newly prepared radioactive sample shows $4$ times the allowed and safe value of radioactivity, the minimum time after which one can work safely with the source is (in $\,h$)

The graph between the instantaneous concentration $(N)$ of a radioactive element and time $(t)$ is:

$A$ radioactive sample decays by $10\%$ in one month. What percentage of the sample will decay in four months (in $\%$)?

An alloy is composed of two radioactive materials $A$ and $B$ having equal weight. The half-lives of $A$ and $B$ are $10 \ yrs$ and $20 \ yrs$ respectively. After time $t$,the alloy was found to consist of $(1/e) \ kg$ of $A$ and $1 \ kg$ of $B$. If the atomic weights of $A$ and $B$ are the same,then the value of $t$ is (Assume $\ln 2 = 0.7$):