Question

A researcher claims that an ancient scroll originated from Greek scholars in about 500 BCE. A measure of its carbon-14 decay rate gives a value that is 89%% of that found in living organisms. How old is the scroll

Answer 1

`963.34\ \text{years}`

Explanation:

`t_(1/2)` = Half life of carbon = 5730 years

`(N)/(N_0)` = Decay rate =
`89\%=(89)/(100)`

Duration of time passed is given by

`t=t_(1/2)(\ln(N)/(N_0))/(\ln(1)/(2))\\\Rightarrow t=5730*(\ln(89)/(100))/(\ln(1)/(2))\\\Rightarrow t=963.34\ \text{years}`

The scroll is
`963.34\ \text{years}` old.