Question

If the half-life of an isotope of cobalt is 60 years. How much of a 3-

gram sample will be left after 300 years?

Answer 1

To determine how much of a 3-gram cobalt isotope sample will remain after 300 years, we apply the half-life principle. After five half-lives (300 years total), 0.09375 grams of the original sample will be left.

Step-by-step explanation:

To calculate the amount of a 3-gram sample of an isotope of cobalt with a half-life of 60 years that will be left after 300 years, we can use the concept of half-lives to determine how much of the substance remains. Since 300 years is five times the half-life of the isotope (300 years / 60 years per half-life = 5 half-lives), we can apply the half-life decay principle to determine the remaining mass.

To calculate the remaining mass after each half-life, we follow these steps:

1. 
   
3. After 1 half-life (60 years): 50% of 3 grams remains = 1.5 grams.
4. 
   
6. After 2 half-lives (120 years): 50% of 1.5 grams remains = 0.75 grams.
7. 
   
9. After 3 half-lives (180 years): 50% of 0.75 grams remains = 0.375 grams.
10. 
    
12. After 4 half-lives (240 years): 50% of 0.375 grams remains = 0.1875 grams.
13. 
    
15. After 5 half-lives (300 years): 50% of 0.1875 grams remains = 0.09375 grams.

Therefore, after 300 years, 0.09375 grams of the original 3-gram sample of the cobalt isotope will remain.