The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at time $t_2$. If $\lambda$ is the decay constant,then which of the following is correct?

The rate of disintegration of a fixed quantity of a radioactive element can be increased by

The half-life of $_{38}^{90} Sr$ is $28$ years. What is the disintegration rate of $15 \; mg$ of this isotope?

Radioactive nuclei $A$ and $B$ disintegrate into $C$ with half-lives $T$ and $2T$. At $t = 0$,the number of nuclei of each $A$ and $B$ is $x$. The number of nuclei of $C$ when the rate of disintegration of $A$ and $B$ are equal is:

After $280$ days,the activity of a radioactive sample is $6000 \, dps$. The activity reduces to $3000 \, dps$ after another $140$ days. The initial activity of the sample in $dps$ is

$A$ 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