A zoologist has found a turtle shell that he believes may be 75000 years old. The shell weighs 10kg. This 10kg of turtle shell would have had an activity of 40 000 Bq when living. If the shell is 75 000 years old. What would be a suitable range for the detector to measure the activity correctly? (Hint: work out how many half lives would have passed in 75 000 years and hence what the count rate should be now).

Carbon dating is a method for determining the age of organic material by measuring the radiation activity of carbon-14. Carbon-14 has a half-life of approximately 5700 years, meaning that every 5700 years, the activity is halved. Knowing this, we can calculate how many half-lives have passed, and what the expected activity is.

If the shell is truly 75,000 years old, then the number of half-lives that have passed since then is:

75,000 / 5700 ≈ 13

So the original activity will have been halved 13 times. The new activity is therefore:

(40,000 Bq) × (1/2)¹³ = 4.88 Bq

Therefore, the detector should be set to a range of 4 to 5 Bq.