If you originally have 10 grams of a radioisotope that has a half-life of 2 years, how much of the radioisotope will remain in 6 years?

If you originally have 10 grams of a radioisotope that has a half-life of 2 years, how much of the radioisotope will remain in 6 years?

• A. 5 grams
• B. 2.5 grams
• C. 1.25 grams
• D. 0.625 grams

Answer: (C)

To determine how much of the radioisotope remains after 6 years, it is important to understand the concept of half-life. The half-life of a substance is the time required for half of the material to decay. In this scenario, the half-life of the radioisotope is 2 years. This means that after 2 years, half of the original amount (10 grams) will have decayed, leaving you with 5 grams. After another 2 years (4 years total), half of the remaining 5 grams will decay again, resulting in 2.5 grams left. After another 2 years (6 years total), half of the remaining 2.5 grams will decay, leaving you with 1.25 grams. Thus, after 6 years, the remaining quantity of the radioisotope is correctly calculated as 1.25 grams. This demonstrates how successive halving occurs with each elapsed half-life, effectively allowing for a straightforward way of calculating the remaining amount at any given interval.

To determine how much of the radioisotope remains after 6 years, it is important to understand the concept of half-life. The half-life of a substance is the time required for half of the material to decay.

In this scenario, the half-life of the radioisotope is 2 years. This means that after 2 years, half of the original amount (10 grams) will have decayed, leaving you with 5 grams. After another 2 years (4 years total), half of the remaining 5 grams will decay again, resulting in 2.5 grams left. After another 2 years (6 years total), half of the remaining 2.5 grams will decay, leaving you with 1.25 grams.

Thus, after 6 years, the remaining quantity of the radioisotope is correctly calculated as 1.25 grams. This demonstrates how successive halving occurs with each elapsed half-life, effectively allowing for a straightforward way of calculating the remaining amount at any given interval.