Half life and its usesHalf life and its uses

No of coins

Start

Throw 1

Throw 2

Throw 3

Throw 4

Throw 5

Throw 6

Throw 7

We are going to start with 2 coins each and throw them all and then count how many had landed with heads facing up and record this. We will then remove those coins that have landed heads up and throw the remaining coins. How many of these will land heads up? Can you predict what would happen to an individual coin?

Number of coins

Number of throws

Half-LifeHalf-Life

The half life is the time taken for half of the The half life is the time taken for half of the radioactive nuclei present to decay.radioactive nuclei present to decay.

Time zero: Number of nuclei, NTime zero: Number of nuclei, N

After one half-life

Time 1: Number of nuclei, N/2Time 1: Number of nuclei, N/2

After two half-lives

Number of nuclei, N/4Number of nuclei, N/4

After three half-lives

Number of nuclei, N/8Number of nuclei, N/8

After four half-lives

Number of nuclei, N/16Number of nuclei, N/16

After five half-lives

Number of nuclei, N/32Number of nuclei, N/32

After five half-lives

Key pointsKey points

Each nucleus in a sample of an isotope Each nucleus in a sample of an isotope decays at random, regardless of what the decays at random, regardless of what the other nuclei are doing.other nuclei are doing.

Radioactive decay is not effected by:Radioactive decay is not effected by:

-Chemical state of the isotope, i.e. whether its -Chemical state of the isotope, i.e. whether its in a compound or as its elementin a compound or as its element

-Temperature or pressure-Temperature or pressure

-Whether it is solid, liquid, gas or in solution-Whether it is solid, liquid, gas or in solution

Key pointsKey points

Half life is: ‘time taken for half the Half life is: ‘time taken for half the radioactive nuclei to decay’.radioactive nuclei to decay’.

It is the same regardless of how many It is the same regardless of how many radioactive nuclei we start with.radioactive nuclei we start with.

The sample never completely disappears, it The sample never completely disappears, it just halves each time, this is why radioactive just halves each time, this is why radioactive isotopes can still be detected today, 4 billion isotopes can still be detected today, 4 billion years after the earth was formed. years after the earth was formed.

ExamplesExamples

IsotopeIsotope Half-lifeHalf-life

Uranium-238 4.5 x 109 years

Carbon-14 5.7 x 103 years

Strontium-90 28 years

Iodine-131 8.1 days

Bismuth-214 19.7 minutes

Polonium-214 1.5 x 10-4 seconds

How to calculate half life

How to calculate half life

How to calculate half life

Half LifeHalf Life

Half LifeHalf Life

The _________ of a sample always _______ over The _________ of a sample always _______ over time. Each time a decay happens ______, ______ time. Each time a decay happens ______, ______ or ______ radiation is emitted. This means a or ______ radiation is emitted. This means a radioactive _______ has decayed. radioactive _______ has decayed. The problem with trying to measure the time for all The problem with trying to measure the time for all the atoms to decay is that the activity never the atoms to decay is that the activity never reaches _____. reaches _____. The half life is the _____ taken for ____ of the The half life is the _____ taken for ____ of the radioactive ______ now present to decay.radioactive ______ now present to decay.An isotope with a ____ half life decays more An isotope with a ____ half life decays more quickly than an isotope with a _____ half life.quickly than an isotope with a _____ half life.

radioactivity decreasesalpha beta

gammanucleus

zero

time halfnuclei

long

short

Uses of radioisotopes in geologyUses of radioisotopes in geology

Radioactive Radioactive parent isotopeparent isotope

Stable daughter Stable daughter isotopeisotope

Half-life Half-life (years)(years)

Potassium-40Potassium-40 Argon-40Argon-40 1.3 x 101.3 x 1099

Rubidium-87Rubidium-87 Strontium-87Strontium-87 4.5 x 104.5 x 101010

Thorium-232Thorium-232 Lead-208Lead-208 1.4 x 101.4 x 101010

Uranium-235Uranium-235 Lead-207Lead-207 7.0 x 107.0 x 1088

Uranium-238Uranium-238 Lead-206Lead-206 4.5 x 104.5 x 1099

Radioactive DatingRadioactive Dating C-14 makes up 1/10,000,000 of the carbon in the air. C-14 makes up 1/10,000,000 of the carbon in the air. This same proportion is found in living things. When they This same proportion is found in living things. When they die the C-14 is trapped inside and gradually decays with a die the C-14 is trapped inside and gradually decays with a half life of 5600 yrs half life of 5600 yrs By measuring the proportion of C-14 left and knowing By measuring the proportion of C-14 left and knowing the half life you can calculate how long ago something was the half life you can calculate how long ago something was living. living.

PRACTICE QUESTION:PRACTICE QUESTION:An axe handle was found to contain 1 part in 40,000,000 C-An axe handle was found to contain 1 part in 40,000,000 C-14. How old is the axe?14. How old is the axe?

The C-14 was originally 1 part in 10,000,000. After 1 half life it would be down to 1 part in 20,000,000 and after 2 half lives it would be down to 1 part in 40,000,000. So the axe handle is 2 half lives old, i.e. 2 x 5600 years = 11,200 years.

Radioactive Dating QuestionRadioactive Dating Question

The half life of C-14 is 5,600 years and C-14 makes The half life of C-14 is 5,600 years and C-14 makes up 1 part in 10,000,000 of the carbon in the air. up 1 part in 10,000,000 of the carbon in the air. Calculate how long ago each of the following was Calculate how long ago each of the following was living material:living material:

a.a. A fossil containing 1 part in 320,000,000 C-14A fossil containing 1 part in 320,000,000 C-14

b.b. A spear handle containing 1 part in A spear handle containing 1 part in 80,000,000 C-1480,000,000 C-14

c.c. An axe handle containing 1 part in An axe handle containing 1 part in 20,000,000 C-1420,000,000 C-14

Remember…Remember…

For these radioisotopes to work as For these radioisotopes to work as geological clocks the following must be met:geological clocks the following must be met:

-Half-life must be known accurately-Half-life must be known accurately

-No movement of parent or daughter isotopes -No movement of parent or daughter isotopes out of or into mineral since crystallisationout of or into mineral since crystallisation

-no resetting of geological clock through -no resetting of geological clock through heating and deformation of the rocks heating and deformation of the rocks (metamorphism)(metamorphism)

Dating rocksDating rocks

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

Dating RocksDating RocksIgneous rocks can be dated if you measure Igneous rocks can be dated if you measure the ratios of uranium-235 and its decay the ratios of uranium-235 and its decay product lead. The half life of uranium-235 is product lead. The half life of uranium-235 is 4.5 billion years. Assuming no lead was 4.5 billion years. Assuming no lead was present when the rock was formed find the present when the rock was formed find the ages of the rocks:ages of the rocks:

a) uranium: lead 1:1a) uranium: lead 1:1b) uranium: lead 75:525b) uranium: lead 75:525c) uranium: lead 1:0c) uranium: lead 1:0d) uranium: lead 75:225d) uranium: lead 75:225

Uses of Carbon-14 datingUses of Carbon-14 dating

Read the green boxes on pages 9-10 for Read the green boxes on pages 9-10 for more examples of where carbon-14 dating more examples of where carbon-14 dating has been used.has been used.

Radioactive tracersRadioactive tracers

As we have learnt more about isotopes a new field As we have learnt more about isotopes a new field of medicine has begun to develop, ‘Nuclear of medicine has begun to develop, ‘Nuclear Medicine’. Medicine’.

Radioisotopes can now be injected into the body Radioisotopes can now be injected into the body to enable detection and treatment for a range of to enable detection and treatment for a range of problems. problems.

The half-life of the isotopes is important so as not The half-life of the isotopes is important so as not to cause unnecessary damage to the cells.to cause unnecessary damage to the cells.

Examples include iodine-131 to detect thyroid Examples include iodine-131 to detect thyroid problems and technetium-99 to detect tumours. problems and technetium-99 to detect tumours.