Question

If you have an organic sample of C - 14 weighing 220g, how long will it take to be reduced to 55g of C-14? Show all the calculations you will use.

a) 2 half-lives
b) 3 half-lives
c) 4 half-lives
d) 5 half-lives

Answer 1

It takes 2 half-lives for a sample of C-14 to reduce from 220g to 55g. With the half-life of C-14 being 5,730 years, the sample will reach 55g after 11,460 years.

Step-by-step explanation:

The question is asking about the time it takes for a sample of Carbon-14 (C-14) to reduce from an initial mass to a quarter of that mass through its radioactive decay process. Since we know that the half-life of C-14 is approximately 5,730 years, we can use this information to calculate the number of half-lives required to reduce the sample from 220g to 55g.

To calculate the number of half-lives (n) needed for the sample to be reduced to 55g, we follow these steps:

• 
  
• Start with the initial amount of 220g.
• 
  
• Realize that after 1 half-life (5,730 years), we'll have half of 220g, which is 110g.
• 
  
• After 2 half-lives, or 2 x 5,730 years, we'll have half of 110g, which is 55g.

Therefore, it will take 2 half-lives for the sample of C-14 to be reduced from 220g to 55g, each half-life being 5,730 years. So the total time is 2 x 5,730 years or 11,460 years.