4.4.2.3 Half-lives and the random nature of radioactive decay

what do radioactive isotopes do

release radiation from the nucleus of their atoms

what is decay

a random process, which cannot be predicted

what is the half life of a radioactive isotopw

the time it takes for the number of nuclei of the isotope in a sample to halve

or the time it takes for the count rate (or activity) from a sample containing the isotope to fall to half its initial level.

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It cannot be predicted when any one nucleus will decay, but the half-life is a constant that enables the activity of a very large number of nuclei to be predicted during the decay.

what is half life

the time it takes for half of the unstable nuclei to decay

the time it takes for the count rate or activity to halve

find the half lives of this graph

To calculate the half-life of a sample, the procedure is:

* Measure the initial activity, *A0*, of the sample
* Determine the half-life of this original activity
* Measure how the activity changes with time

long half life

decays slowly

o The source remains weakly radioactive for a long period of time o Americium has a half-life of 432 years  It is an alpha emitter, and used in smoke alarms  It is emitted into the air around the alarm, and does not reach far because alpha is weakly penetrating  If smoke reaches the alarm, the amount of alpha particles in the surrounding air drops  This causes the alarm to sound o It is suitable because it will not need to be replenished, and its weak activity means it won’t be harmful to anyone

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Long half-life, less active sample, stability is achieved after a longer time

short half life

nuclei decay at a faster rate- wont take log for the number of the original isotope to halve

The source presents less of a risk, as it does not remain strongly radioactive

o This means initially it is very radioactive, but quickly dies down

o So presents less of a long-term risk

Short half-life, more active sample, less stable sample initially

Stability is achieved in a shorter time

What does this graph show us?

•The number of surviving nuclei decreases with time

•Activity depends on the number of surviving nuclei so activity decreases with time

•The rate of decay is high initially but reduces with time

•In reality, activity never actually decreases to zero

•All radioactive samples produce the same characteristic graph shape

\- So if 80 atoms falls to 20 over 10mins, the half-life?

80/2 = 40 o

40/2 = 20

– so two half lives in 10mins

So half-life is 5mins

Net Decline

\- Calculate the ratio of net decline of radioactive nuclei after X half-lives o Half the initial number of nuclei, and keep doing so X number of times

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parctical method

1. count the number of nuclei in your sample to start and record this time at 0
2. throw them gently onto a tray
3. remove any that land with the ‘black side’ upwards- these are decayed nuclei. count the remaining ones and record them for each throw
4. each throw represents an hour of time. continue until they have all decayed

What is the relevance of half-life?

Carbon dating

All living things contain a tiny amount of the radioactive carbon-14

When living things die, they no longer absorb carbon-14

the amount of carbon-14 begins to reduce due to radioactive decay by beta decay

The half-life of carbon-14 is 5730 years

By measuring the levels of carbon-14 remaining in a piece of wood, cloth or body it is possible to determine the age of the item

Uranium dating

•This is used to find the age of igneous rocks

•Igneous rocks with a half-life of 4500 million years

•Each uranium atoms decays into an atom of lead

•The age of the sample can be worked out by measuring the number of atoms of uranium and lead

Count rate after n half-lives=

(Initial count rate)/2^n

Activity after n half-lives=

(Initial activity)/2^n

Number of half-lives=

(Total time)/(Time taken for one half-life)

Net decline=

(Reduction in activity)/(Original activity)

Reduction in activity=

Original activity-final activity