The age of a tree is determined using the radio-isotope of:

The half-life of $Ra^{226}$ is $1620$ years. Calculate the number of atoms that decay in one second in $1 \ g$ of radium (Avogadro number $= 6.023 \times 10^{23}$).

Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0$, they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of:

In a radioactive element,the fraction of the initial amount remaining after its mean lifetime is:

The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at a later time $t_2$. Its decay constant is $\lambda$. Which of the following relations is correct?

The half-life of a radioactive substance is $20 \, \text{minutes}$. The approximate time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{3}{4}$ of it has decayed and time $t_1$ when $\frac{1}{4}$ of it has decayed is: