Chemistry

Problem

10\,\text{g}

fragment of bone is placed inside a radiation detector that registers

240

counts in

20\,\text{min}

. A blank run with an empty vial under identical conditions gives

30

counts in

20\,\text{min}

. The detector has an efficiency of

25\%

(it records one in every four disintegrations that actually occur inside the sample). Fresh living bone has a specific activity of

0.25\,\text{Bq g}^{-1}

for

^{14}\text{C}

. The half-life of

^{14}\text{C}

5730\,\text{y}

. a. (i) Calculate the net activity per gram of the bone sample after correcting for background and detector efficiency. b. (ii) Using this activity, estimate the age of the bone. c. (iii) If the background correction in part (i) were neglected, what age would be obtained? Hence find the percentage error introduced by ignoring background radiation.

Intuitive explanation

The key is separating the true signal from background noise, then using radioactive decay's relationship between activity, half-life, and age. Subtract the blank counts to find the actual disintegrations from the bone sample, correct for detector efficiency to get the true activity, and compare it to the activity of fresh bone—the ratio tells you how many half-lives have elapsed since the organism died. This is the foundation of radiocarbon dating.

Intuitive explanation

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