Question

Humans take in the radioactive isotope carbon-14 from their food. After their death, th proportion of carbon-14 in their bones can be used to tell how long it is since they die Carbon-14 has a half-life of 5700 years. (i) A bone in a living human contains 80 units of carbon-14. An identical bone take from a skeleton found in an ancient burial ground contains 5 units of carbon-14 Calculate the age of the skeleton. Show clearly how you work out your answe Age of skeleton = ​

Answer 1

To calculate the age of the skeleton using carbon dating, we determine the number of half-lives needed for 80 units of carbon-14 to decay to 5 units. After four half-lives, which totals 22,920 years, we get the approximate age of the skeleton.

Step-by-step explanation:

To calculate the age of the skeleton using carbon dating, we first recognize that the original amount of carbon-14 (C-14) in a living bone is given as 80 units. After the organism's death, this isotope decays with a half-life of about 5,730 years. The skeleton in question has 5 units of C-14 remaining. We can calculate the number of half-lives that have passed to get down to 5 units from 80 units.

Each half-life reduces the amount of C-14 by half. Let's calculate how many half-lives it takes for 80 units to become 5 units:

First half-life: 80 / 2 = 40 units
Second half-life: 40 / 2 = 20 units
Third half-life: 20 / 2 = 10 units
Fourth half-life: 10 / 2 = 5 units

It took four half-lives to get from 80 units to 5 units of C-14. Since one half-life is 5,730 years, we multiply this value by the number of half-lives:

Age of the skeleton = 4 (half-lives) × 5730 years/half-life = 22920 years.

Thus, the skeleton is approximately 22,920 years old.