The activity of a radioactive substance can be represented by various units. Select the correct option.

Which is the correct expression for half-life?

Two radioactive materials $X_1$ and $X_2$ have decay constants $5\lambda$ and $\lambda$ respectively. Initially,they have the same number of nuclei. The ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $\frac{1}{e}$ after a time:

Decay constants of two radioactive samples $A$ and $B$ are $15x$ and $3x$ respectively. They have an equal number of initial nuclei. The ratio of the number of nuclei left in $A$ and $B$ after a time $t = \frac{1}{6x}$ is

The decay constant of radium is $\lambda$. By a suitable process,its compound radium bromide is obtained. The decay constant of radium bromide will be:

For a radioactive material,its activity $A$ and rate of change of its activity $R$ are defined as $A = -\frac{dN}{dt}$ and $R = -\frac{dA}{dt}$,where $N(t)$ is the number of nuclei at time $t$. Two radioactive sources $P$ (mean life $\tau$) and $Q$ (mean life $2\tau$) have the same activity at $t = 0$. Their rates of change of activities at $t = 2\tau$ are $R_P$ and $R_Q$,respectively. If $\frac{R_P}{R_Q} = \frac{n}{e}$,then the value of $n$ is