The half-life of a radioactive nucleus is $5$ years. The fraction of the original sample that would decay in $15$ years 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 $.... \, \text{sec}$.

$A$ radioactive nucleus $n_2$ has $3$ times the decay constant as compared to the decay constant of another radioactive nucleus $n_1$. If initial number of both nuclei are the same,what is the ratio of number of nuclei of $n_2$ to the number of nuclei of $n_1$,after one half-life of $n_1$?

$A$ radioactive sample has an average life of $30 \, ms$ and is decaying. $A$ capacitor of capacitance $200 \, \mu F$ is first charged and later connected with a resistor $R$. If the ratio of charge on the capacitor to the activity of the radioactive sample is fixed with respect to time,then the value of $R$ should be $.... \, \Omega$.

$A$ radioactive nucleus with a decay constant $\lambda = 0.5/s$ is being produced at a constant rate of $P = 100\, nuclei/s$. If at $t = 0$ there were no nuclei,the time when there are $N = 50\, nuclei$ is:

$N$ atoms of a radioactive element emit $n$ alpha particles per second. The half-life of the element is: