Question

you want to use radiometric dating to determine the age of a specimen. you use isotope z, which has a half-life of 645 years. you measure your sample and find that 1/16 of the original amount of isotope z is present. how old is the sample?

Answer 1

By determining that 4 half-lives have passed for isotope Z to reach 1/16 of its original amount, and with each half-life being 645 years, the sample is calculated to be 2580 years old.

Step-by-step explanation:

To determine the age of a specimen using radiometric dating and isotope Z with a half-life of 645 years, we can apply the concept of half-lives. Since only 1/16 of the original amount of isotope Z is present, we must determine how many half-lives have passed. Each half-life reduces the amount of the isotope by half, so we can use the formula 1/(
`2^n` remaining amount to find n, the number of half-lives.

Applying this formula: 1/(2^n) = 1/16. By solving for n, we find that n equals 4, which means that four half-lives have passed. To find the total age of the sample, we multiply the number of half-lives by the length of one half-life. Age of sample = number of half-lives × half-life of isotope, so the age of the sample is 4 × 645 years, which is 2580 years. Therefore, the sample is 2580 years old.

Answer 2

2580 years

Step-by-step explanation:

Since isotope Z has a half-life of 645 years, that means after 645 years, half of the original amount of isotope Z will decay. So, if 1/16 of the original amount is present, that means there have been 4 half-lives (since 2^4 = 16).

Each half-life is 645 years, so 4 half-lives is 4 x 645 = 2580 years.

Therefore, the age of the sample is 2580 years.