The correct answer is option 4, Uranium-238.

To understand why uranium-238 has the maximum half-life period, it is important to first understand what half-life means. Half-life is the time taken for half of the atoms in a radioactive substance to decay. In other words, it is the time it takes for the initial number of radioactive atoms to reduce by half.

Uranium-238 is a radioactive substance commonly found in rocks and soil. It has a very long half-life period of about 4.5 billion years. This means that it takes 4.5 billion years for half of the uranium-238 atoms to decay.

Carbon-14 (option 1) has a much shorter half-life of about 5,730 years. Plutonium-239 (option 2) has a half-life of about 24,110 years. Radium-226 (option 3) has a half-life of about 1,601 years.

Therefore, among the given options, uranium-238 has the longest half-life period, making it the radioactive substance with the maximum half-life. This long half-life makes uranium-238 useful for dating geological materials and studying the history of the Earth.