Final answer:
After 150 years, which equals two half-lives of 75 years each, 25% of the radioactive substance would remain, since the amount is halved with each half-life.
Step-by-step explanation:
The question involves calculating the remaining fraction of a radioactive substance after a certain period of time, which involves the concept of half-life. The half-life is defined as the time it takes for half of the radioactive nuclei to decay.
If the half-life of a substance is 75 years, then after one half-life (75 years) only 50% of the original amount will remain. After two half-lives (150 years), another half of the remaining 50% will decay, leaving us with 25% of the original amount.
To find the fraction of the substance that remains after 150 years, you simply apply the concept that with each passing half-life, the remaining amount of the substance is halved.
The fraction of a radioactive substance that will remain after a certain time can be determined by calculating the number of half-lives that have passed. In this case, the half-life of the substance is 75 years.
Since 150 years is exactly two half-lives, the remaining fraction can be calculated as (1/2) * (1/2) = 1/4. Therefore, 1/4 of the radioactive substance will remain after 150 years.