LOJ Feb 2004

Radioactivity 6

Half Life

LOJ Feb 2004

Half Life

The half-life of a radioactive substance:• is the time it takes for the number of parent atoms in a sample to halve;• is the time it takes for the count rate from the original substance to fall to half its initial level.

During one half-life, half of the radioactive atoms initially present in a sample decay. This idea can be used to date materials.

LOJ Feb 2004

Graphs

• A plot of the activity of a sample against time shows exponential decay

• From such a graph you should be able to find the half life of the sample

LOJ Feb 2004

Equipment needed to measure

radioactive decay

LOJ Feb 2004

LOJ Feb 2004

LOJ Feb 2004

LOJ Feb 2004

Remember when Plotting Graphs

• Deduct background rate from the experiment count you are given – call this ‘corrected count rate’

• Plot corrected count rate on the Y-axis and time on the X-axis.

• Draw a best fit smooth curve through the points. Not a dot-to-dot straight line joining!

LOJ Feb 2004

Remember when Plotting Graphs

• At least two readings of half life should be found from the graph.

• Indicate clearly how you have used the graph with dashed guide lines – use colour

• Repeats should be done to check the answer is correct - they should be very similar.

• The average value of these should be quoted as your answer

LOJ Feb 2004

Dating Rocks• The older a sample of a particular

radioactive material, the less radiation it emits. This idea can be used to date materials, including rocks.

• During one half-life, half of the radioactive atoms initially present in a sample decay. This idea can be used to date materials.

LOJ Feb 2004

Dating Rocks

• Uranium isotopes, which have a very long half-life, decay via a series of relatively short-lived radioisotopes to produce stable isotopes of lead. The relative proportions of uranium and lead isotopes in a sample of igneous rock can, therefore, be used to date the rock.

LOJ Feb 2004

Dating Rocks

•The proportions of the radioisotope potassium-40 and its stable decay product argon can also be used to date igneous rocks from which the gaseous argon has been unable to escape.

LOJ Feb 2004

Carbon Dating

• Methods of finding out the age of artefacts that contain materials that were once alive.

• When it dies a living organism takes in no more carbon from the atmosphere and the percentage of C-14 will decrease. The ratio of C-14 to total carbon is found and from this the age can be calculated.

LOJ Feb 2004

How it works• Carbon Dating measures the remaining

amount of the radioactive isotope carbon-14 in organic matter. It can be used to date specimens as old as 35,000 years.

• During its lifetime a biological entity (plant or animal) takes an active part in the carbon cycle and it contains the same proportion of the isotope as the atmosphere does (about one ten millionth of the carbon is carbon-14).

LOJ Feb 2004

LOJ Feb 2004

Carbon Dating

• The death of an organism terminates the incorporation of this isotope into the fabric of the entity. From the time of death onwards the proportion of carbon-14 decreases as it decays into nitrogen.

LOJ Feb 2004

The maths• By calculating the

ratio of C-14 to total carbon in a sample of the artefact it is possible to work out its age. The half-life of carbon-14 is 5,600 years.

• This data could be plotted on a graph

  C-14 in total carbon

Age (years)

Initial Value

1 part in 10 million

0

After one half-life

0.5 parts in 10 million 

5,600

After two half-lives

0.25 parts in 10 million 

11,200

After three half-lives

0.125 parts in 10 million

16,800

After four half-lives

0.0625 parts in 10 million

22,400

LOJ Feb 2004

Finding the Age of Rocks• The most common and accepted method

of 'absolute geologic dating' (establishment of actual age) is based on the natural radioactivity of certain minerals found in rocks.

• As the rate of radioactive decay of any particular isotope is known, the age of a specimen can be worked out from the ratio of the remaining isotope and its decay product.

LOJ Feb 2004

LOJ Feb 2004

Dating of Igneous Rocks (Using Uranium Content)

• Geologists use this method to date igneous rock samples. If you look carefully at the half-lives of isotopes in the Uranium series you appreciate that the Uranium has a much longer half-life than any of the others.

• Uranium eventually decays to lead.

LOJ Feb 2004

Dating of Igneous Rocks (Using Uranium Content)

• So, by comparing the proportion of Uranium in the rock to the proportion of Lead produced by its decay you can work out how many half-lives it has been decaying.

• Then by using the half-life of Uranium you can work out the time involved.

LOJ Feb 2004

  Percentage of

Uranium

Percentage of Lead

Ratio of Uranium to Lead

Age (millions of years)

Initial Value

100.00% 0.00% 01:00 0

After one half-life

50.00% 50.00% 01:01 4,500

After two half-lives

25.00% 75.00% 01:03 9,000

After three half-lives

12.50% 87.50% 01:07 13,500

After four half-lives

6.25% 93.75% 01:15 18,000