An important example of beta-decay is that of 14C, which is used inradio-active dating:
14C ? 14N + ?- + ve
The half-life of this decay is 5730 years. The radioactive isotope14C nuclei is produced in the upper atmosphere from nuclearreactions caused by cosmic rays. The chemical behavior of carbonatoms with 14C nuclei is the same as those with ordinary 12Cnuclei, e.g., atoms with these nuclei combine with oxygen to formCO2 with the atmosphere, the ratio of 14C to 12C in a livingorganism is the same as the equilibrium ratio in the atmosphere,which is about 1.3x10-12. When an organism dies, it no longerabsorbs 14C from the atmosphere, so that the ratio 14C/12Ccontinually decreases due to the radioactive decay of 14C. Ameasurement of the decay rate per gram of carbon thus allows thecalculation of the time of death of organism.
(a) Using the above information, show that the decay rate per gramof carbon of a living orgamism is 15 decays per minute per gram ofcarbon.
(b) A bone containing 200 g of carbon has a beta-decay rate of 400decays/min. How old is the bone?
An important example of beta-decay is that of 14C, which is used inradio-active dating:
14C ? 14N + ?- + ve
The half-life of this decay is 5730 years. The radioactive isotope14C nuclei is produced in the upper atmosphere from nuclearreactions caused by cosmic rays. The chemical behavior of carbonatoms with 14C nuclei is the same as those with ordinary 12Cnuclei, e.g., atoms with these nuclei combine with oxygen to formCO2 with the atmosphere, the ratio of 14C to 12C in a livingorganism is the same as the equilibrium ratio in the atmosphere,which is about 1.3x10-12. When an organism dies, it no longerabsorbs 14C from the atmosphere, so that the ratio 14C/12Ccontinually decreases due to the radioactive decay of 14C. Ameasurement of the decay rate per gram of carbon thus allows thecalculation of the time of death of organism.
(a) Using the above information, show that the decay rate per gramof carbon of a living orgamism is 15 decays per minute per gram ofcarbon.
(b) A bone containing 200 g of carbon has a beta-decay rate of 400decays/min. How old is the bone?
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