Final answer:
The correct answer is none of the above. After two half-lives of a radioactive substance with a half-life of 75 years, 25% of the substance remains. The question's provided answer options seem to be incorrect as no option matches the correct calculation.
Step-by-step explanation:
The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, the half-life is 75 years. To find out what fraction of the substance remains after 150 years, which is two half-lives (150 years ÷ 75 years/half-life = 2 half-lives), we can use the formula for determining the remaining amount of a radioactive isotope after a given number of half-lives. The formula is: remaining fraction = ½n, where 'n' is the number of half-lives.
After the first half-life, half of the substance remains, so we have ½ remaining. After the second half-life, we take half of that remaining amount, which is ½ of ½, equaling ½2 or 0.25 (25%). Therefore, the correct answer is option D. 0.34. However, since 0.25 is not among the options and 0.25 is not equal to 0.34, we must recognize an error in the options provided. The expected correct option should be E. None of the above, but since it's not available, we should consider the options are incorrect.