Some fossil bones contain 1/8 of their original amount of carbon-14.how many half-lives have passed? how old are the bones?

3 half-lives have passed.

The bones are 17 190 years old.

Explanation:

The half-life of a radioactive element is the time required for the substance to lose half of its initial activity. In other words, the half-life is denoted by this symbol

Let's take the half-life of carbon as

After a certain number of years, the activity degenerates to half of the original activity. So it will be

After some years, the activity will be

Thus three half-lives have passed. A simple formula to remember the pattern is to use the exponential expression :

solving for x gives x = 3

hence there half-lives.

For carbon,

since there half-lives have passed, the age of the sample will be

The sample will be 17 190 years.

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