The curve between the activity $A$ of a radioactive sample and the number of active atoms $N$ is

For a certain radioactive process,the graph between $\ln R$ and $t \, (\text{sec})$ is obtained as shown in the figure. Then the value of the half-life for the unknown radioactive material is approximately $.... \, \text{sec}$.

$A$ nuclear power plant supplying electrical power to a village uses a radioactive material of half-life $T$ years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is $12.5 \%$ of the electrical power available from the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of $n T$ years,then the value of $n$ is

$A$ radioactive nucleus can decay by two different processes. The half-lives of the first and second decay processes are $5 \times 10^3$ years and $10^5$ years respectively. Then,the effective half-life of the nucleus is

The half-life of $^{238}_{92}U$ undergoing $\alpha$-decay is $4.5 \times 10^{9} \text{ years}$. What is the activity of a $1 \text{ g}$ sample of $^{238}_{92}U$?

Half-life of a radioactive substance is $20 \ min$. The difference between the points of time when it is $33\%$ disintegrated and $67\%$ disintegrated is approximately ........... $min$.