#
Questions on Radioactivity: Carbon Dating

**Q1.
**The carbon content of living trees includes a small proportion of carbon-14, which is a radioactive isotope. After a tree dies, the proportion of carbon-14 in it decreases due to radioactive decay.

(a)

(i) The half-life of carbon-14 is 5740 years.

Calculate the radioactive decay constant in yr^{−1} of carbon-14.

**(1 mark)**

(ii) A piece of wood taken from an axe handle found on an archaeological site has 0.375 times as many carbon-14 atoms as an equal mass of living wood.

Calculate the age of the axe handle in years.

**(3 marks) **

(b) Suggest why the method of carbon dating is likely to be unreliable if a sample is:

(i) less than 200 years old,

(ii) more than 60 000 years old.

**(2 marks) **

**(Total 6 marks)**

**Q2.**

The age of an ancient boat may be determined by comparing the radioactive decay of from living wood with that of wood taken from the ancient boat.

A sample of 3.00 × l0^{23} atoms of carbon is removed for investigation from a block of living wood. In living wood one in 10^{12} of the carbon atoms is of the radioactive isotope , which has a decay constant of 3.84 × 10^{–12} s^{–1}.

(a) What is meant by the decay constant?

**(1 mark)**

(b) Calculate the half-life of the wood in years, giving your answer to an appropriate number of significant figures.

1 year = 3.15 × 10^{7} s

**(3 marks) **

(c) Show that the rate of decay of the atoms in the living wood sample is 1.15 Bq.

**(2 marks) **

(d) A sample of 3.00 × 10^{23} atoms of carbon is removed from a piece of wood taken from the ancient boat.

The rate of decay due to the atoms in this sample is 0.65 Bq.

Calculate the age of the ancient boat in years.

**(3 marks) **

(e) Give two reasons why it is difficult to obtain a reliable age of the ancient boat from the carbon dating described.

**(2 marks) **

**(Total 11 marks)**

**Q3.**

The age of a piece of bone recovered from an archaeological site may be estimated by ^{14}C dating.

All living organisms absorb ^{14}C but there is no further intake after death. The proportion of ^{14}C is constant in living organisms.

A 1 g sample of bone from an archaeological site has an average rate of decay of 5.2 Bq due to ^{14}C.

A 1 g sample of bone from a modern skeleton has a rate of decay of 6.5 Bq. The counts are corrected for background radiation.

Calculate the age, in years, of the archaeological samples of bone.

*Half-life of *^{14}C = 5730 years

**(4 marks)**