Three-fourths of the active nuclei decay in a radioactive sample in $3/4 \, s$. The half-life of the sample is:

Half-lives of two radioactive nuclei $A$ and $B$ are $10 \, minutes$ and $20 \, minutes$,respectively. If,initially,a sample has an equal number of nuclei,then after $60 \, minutes$,the ratio of the number of decayed nuclei of $A$ and $B$ will be:

The initial activity of a radioactive element is $1600$. After $t = 8 \, s$,the activity becomes $100$. What is the activity at $t = 6 \, s$?

An element $X$ with a half-life of $1.4 \times 10^9$ years decays to form another stable element $Y$. $A$ sample is taken from a rock that contains both $X$ and $Y$ in the ratio $1:7$. If at the time of formation of the rock,$Y$ was not present in the sample,then the age of the rock in years is

Write the definition of half-life of a radioactive substance and obtain its relation to the decay constant.

The activity of a sample reduces from $A_0$ to $A_0 / \sqrt{3}$ in one hour. The activity after $3$ hours more will be