A radioactive substance has a half-life of four months. Three-fourth of the substance would decay in

Half-life is the time required for half of a radioactive sample to decay [1]. For exponential radioactive decay, the remaining fraction after n half-lives is (1/2)^n, so after one half-life 1/2 remains, after two half-lives 1/4 remains, etc. . “Three-fourth of the substance would decay” means only one-fourth (1/4) remains. Setting (1/2)^n = 1/4 gives n = 2 half-lives. With a half-life of 4 months, two half-lives correspond to 2 × 4 = 8 months. Therefore, three-fourths of the substance will have decayed after 8 months.

Sources

1. [1] Environment, Shankar IAS Acedemy .(ed 10th) > Chapter 5: Environmental Pollution > Period of Radioactivity > p. 83