In 24 days a radioactive isotope decreases in mass from 64g to 2g. What is the half life of the radioactive material

Answer Details

The half-life of a radioactive substance is the time it takes for half of the initial mass of the substance to decay. Let's find the fraction of the initial mass remaining after 24 days: mass remaining/mass at start = (2g/64g) = 1/32 This means that after one half-life, the mass remaining would be half of the initial mass, or (1/2) x 64g = 32g. After two half-lives, the mass remaining would be half of 32g, or 16g. Similarly, after three half-lives, the mass remaining would be 8g, and after four half-lives, the mass remaining would be 4g. Since the mass remaining after 24 days is 1/32 of the initial mass, we know that the number of half-lives that have passed is 5, because 2 raised to the 5th power (2^5) is 32. Therefore, the half-life of the substance is 24 days / 5 = 4.8 days. So the correct option is (d) 4.80 days.