# Half Life

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## Half Life

-Half life is a measure of the time it takes for a radioactive substance to decay

The radioactivity of a sample always decreases over time

1. This is pretty obvious when you think about it. Each time a decay happens and an alpha, beta or gamma is given off. It means one more radioactive nucleus has disappeared.
2. Obviously as the unstable nuclei all steadily disappear, the activity as a whole will decrease. So the older a sample becomes the less radiation it will emit

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## Half Life

3. How quickly the activity decreases varies a lot. For some isotopes it takes just a few hours before nearly all the unstable nuclei have decayed. Others last for millions of years.

4. The problem with trying to measure this is that the activity never reaches zero, which is why we have to use the idea of half life to measure how quickly the activity drops off.

5. LEARN "HALF LIFE IS THE TIME TAKEN FOR HALF OF THE NUCLEI NOW PRESENT TO DECAY"

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## Half Life

6. A short half life means the activity falls quickly becaue lots of the nuclei decay quickly

7. A long half life means the activity falls slowly because most of the nuclei don't decay for a long time - they just sit there, basically unstable but kind of biding their time

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## Half Life

Half Life Questions

1. The activity of a radioisotope is 640cpm (counts per minute). Two hours later it has fallen to 4cpm (counts per minute) Find the half life of the sample

ANSWER                        after one             after two            after three              after four
INITIAL COUNT   ( /2 )         half life     (/2)    half lives   (/2)    half lives       (/2)      half lives

640                                     320                     160                   80                          40

It takes four half lives for the activity to fall from 640 to 40. Hence two hours represents four half lives, so the half-life is 30 minutes.

You can measure the half-life of a radioactive substance using a G-M tube and a counter.

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## Measuring the half-life of a sample using a graph

1. This can only be done by taking several readings of count rate, usually using a G-M tube and counter

2. The results can then be plotted as a graph which will always be shaped like the one below (look at notes)

3. The half-life is found from the graph by finding the time interval on the bottom axis corresponding to a halving of the activity on the virutal axis.

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## Background Radiation should be subtracted

One trick you need to know is about background radiation. This enters the G-M tube along with radiation from the sample giving a reading higher than the activity of the sample.

The solution is to measure the background count first and then subtract it from every reading you get, before plotting the results on the graph.

Half Lives Always Make Curved Graphs
- The radioactivity of a sample always goes down over time because every time a nucleus decays the sample gets smaller, so there are fewer nuclei left to decay. The result is that decay always form nice curves.

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