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Half lives

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Half lives

The half life is the time it takes for the concentration of a substance to decline to half its initial value.

- After two half lives;
- ½ + ½ (½ ) = ¾ will have reacted.
- Leaving only ¼ of the initial concentration.
- After three half lives;
- ½ + ½ (½ ) + ½[½ (½ )] = 7/8 will have reacted.
- Leaving only 1/8 of the initial value.
- After four half lives;
- ½ + ½ (½ ) + ½[½ (½ )] +½{½[½ (½ )]} =15/16 will have reacted.
- Leaving only 1/16 of the initial value.

- It has a half life of 5,730 years
- This means that after 5,730 years have passed only half of the original amount of C14 will remain.
- After 2 x 5730 = 11,460 years there will be ½ x ½ = ¼.
- After 3 x 5730 = 17190 years there will be ½ x ½ x ½ = 1/8…..

- C14 is made by the action of cosmic rays.
- Life is based on carbon.
- Whilst organisms are alive C14 will be absorbed at the same rate as C12.
- As C14 decays it is continually replaced.
- But after death no more C14 is absorbed.
- It is as if a stop clock is started.
- Archaeologists have only to measure the C14 in bones, wood, hair…. to date them.

- The technique can be used for objects up to 48,000 years old.
- But when the ages of historic artefacts several millennia old were compared to the radiocarbon dates they were found to be too young.
- It seems that C14 is not always produced at the same rate.
- So the dates have been calibrated using the wood of the Bristlecone Pine, which lives for over 7,000 years!

- For a first order reaction the half life is constant.
- The time taken for the concentration to fall from the initial value to ½, from ½ to ¼, from ¼ to 1/8 …is exactly the same.
- t½= 0.693 / k
- Where k = rate constant.
- Half lives can be determined by plotting concentration of a reactant against time then measuring the time take for the initial concentration to halve.

- Second order half lives are not constant.
- A basic plot of concentration against time starts off as a much steeper curve, then levels off.
- This means that the half lives become progressively longer.

- NB For a zero order reaction the rate is independent of the concentration.
- Thus a plot of concentration against time is a straight line, rather than a curve.