Different radioactive nuclides decay into their respective daughter nuclides at distinct rates. Some of the nuclides decay briskly, while others decay gradually. The time it consumes for half of the parent nuclide in a radioactive sample to decay to the daughter nuclides is known as the half-life of the radioactive sample.
The nuclides, which decay briskly exhibit short half-lives and are very active. The half-life can be utilized to find the rates of radioactive decay. In the given question, the half-lives of various nuclides are given. So, the order to the most active (shortest half-life or largest number of decays per second) to least reactive (largest half-life or the smallest number of decays per second) is:
Tc-99m > Y-90 > In-111 > I-131