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==Key Stage 4Foundation==
===Meaning===
[[File:HalfLifeGraph1.png|right|300px|thumb|A [[graph]] showing the [[fraction]] of [[Unstable Isotope|unstable isotope]] left compared to the '''half life'''.]]
| style="height:20px; width:300px; text-align:center;" |
'''Half Life''' = 6 [[hour]]s
|}
===Calculating Half Life===
{| class="wikitable"
|-
| style="height:20px; width:300px; text-align:center;" |An [[isotope]] had a [[Count Rate|count rate]] of 200Bq and 90 days later has a [[Count Rate|count rate]] of 25. Calculate the '''half life''' of this [[isotope]].
| style="height:20px; width:300px; text-align:center;" |A [[radioactive]] [[sample]] begins with 224 [[atom]]s of an [[Unstable Isotope|unstable isotope]] 18 [[minute]]s later there are only 14 [[atom]]s of the [[Unstable Isotope|unstable isotope]] left. Calculate the '''half life''' of this [[isotope]].
|-
| style="height:20px; width:300px; text-align:center;" |'''1. Identify how many times the [[Count Rate|count rate]] has halved.'''
<math>200 \div 2 = 100</math>
<math>100 \div 2 = 50</math>
<math>50 \div 2 = 25</math>
The [[Count Rate|count rate]] has halved 3 times.
| style="height:20px; width:300px; text-align:center;" |'''1. Identify how many times the number of [[Unstable Isotope|unstable]] [[atom]]s has halved.'''
<math>224 \div 2 = 112</math>
<math>112 \div 2 = 56</math>
<math>56 \div 2 = 28</math>
<math>56 \div 2 = 28</math>
The number of [[Unstable Isotope|unstable]] [[atom]]s has halved 4 times.
|-
| style="height:20px; width:300px; text-align:center;" |'''2. Divide the time taken by the number of times the [[Count Rate|count rate]] has halved.'''
<math>90 \div 3 = 30</math>
'''Half Life''' = 30 days.
| style="height:20px; width:300px; text-align:center;" |'''2. Divide the time taken by the number of times the number of [[Unstable Isotope|unstable]] [[atom]]s has halved.'''
<math>18 \div 4 = 4.5</math>
'''Half Life''' = 4.5 [[minute]]s
|}
===Finding Half Life and Count Rate from a Table===
{| class="wikitable"
| style="height:20px; width:100px; text-align:center;" |Time /s
| style="height:20px; width:50px; text-align:center;" |0
| style="height:20px; width:50px; text-align:center;" |10
| style="height:20px; width:50px; text-align:center;" |20
| style="height:20px; width:50px; text-align:center;" |30
| style="height:20px; width:50px; text-align:center;" |40
| style="height:20px; width:50px; text-align:center;" |50
| style="height:20px; width:50px; text-align:center;" |60
| style="height:20px; width:50px; text-align:center;" |70
| style="height:20px; width:50px; text-align:center;" |80
|-
| style="height:20px; width:100px; text-align:center;" |Count rate /Bq
| style="height:20px; width:50px; text-align:center;" |1000
| style="height:20px; width:50px; text-align:center;" |707
| style="height:20px; width:50px; text-align:center;" |500
| style="height:20px; width:50px; text-align:center;" |353
| style="height:20px; width:50px; text-align:center;" |250
| style="height:20px; width:50px; text-align:center;" |176
| style="height:20px; width:50px; text-align:center;" |125
| style="height:20px; width:50px; text-align:center;" |88
| style="height:20px; width:50px; text-align:center;" |62
|}
1. Find the '''half life''' of this [[sample]] of [[radioactive]] [[isotope]].
:The '''half life''' of of this [[sample]] of [[radioactive]] [[isotope]] can be found by halving the initial count rate.
:1000/2 = 500Bq
:The [[isotope]] took 20 seconds to half in [[Count Rate|count rate]]:
:'''Half life''' = 20 [[seconds]].
2. Predict the [[Count Rate|count rate]] at 90 seconds.
:Since the '''half life''' is 20 seconds the [[Count Rate|count rate]] 20 seconds earlier can be halved. :At 70 seconds the [[Count Rate|count rate]] was 88Bq. Therefore at 90 seconds the [[Count Rate|count rate]] would be:
:88/2 = 44Bq
3. Predict what the [[Count Rate|count rate]] was 10 seconds before the [[sample]] was first tested.
:Since the '''half life''' is 20 seconds the [[Count Rate|count rate]] 20 seconds later can be doubled. :At 10 seconds the [[Count Rate|count rate]] was 707Bq. Therefore at -10 seconds the [[Count Rate|count rate]] would have been:
:707x2= 1414Bq
{| class="wikitable"
| style="height:20px; width:100px; text-align:center;" |Time /min
| style="height:20px; width:50px; text-align:center;" |0
| style="height:20px; width:50px; text-align:center;" |1
| style="height:20px; width:50px; text-align:center;" |2
| style="height:20px; width:50px; text-align:center;" |3
| style="height:20px; width:50px; text-align:center;" |4
| style="height:20px; width:50px; text-align:center;" |5
| style="height:20px; width:50px; text-align:center;" |6
| style="height:20px; width:50px; text-align:center;" |7
| style="height:20px; width:50px; text-align:center;" |8
|-
| style="height:20px; width:100px; text-align:center;" |Count rate /Bq
| style="height:20px; width:50px; text-align:center;" |5000
| style="height:20px; width:50px; text-align:center;" |3968
| style="height:20px; width:50px; text-align:center;" |3150
| style="height:20px; width:50px; text-align:center;" |2500
| style="height:20px; width:50px; text-align:center;" |1984
| style="height:20px; width:50px; text-align:center;" |1575
| style="height:20px; width:50px; text-align:center;" |1250
| style="height:20px; width:50px; text-align:center;" |992
| style="height:20px; width:50px; text-align:center;" |788
|}
1. Find the '''half life''' of this [[sample]] of [[radioactive]] [[isotope]].
:The '''half life''' of of this [[sample]] of [[radioactive]] [[isotope]] can be found by halving the initial count rate.
:5000/2 = 2500Bq
:The [[isotope]] took 3 [[minute]]s to half in [[Count Rate|count rate]]:
:'''Half life''' = 3 [[minute]]s.
2. Predict the [[Count Rate|count rate]] at 9 [[minute]]s.
:Since the '''half life''' is 3 [[minute]]s the [[Count Rate|count rate]] 3 [[minute]]s earlier can be halved.
:At 6 [[minute]]s the [[Count Rate|count rate]] was 1250Bq. Therefore at 9 [[minute]]s the [[Count Rate|count rate]] would be:
:1250/2 = 625Bq
3. Predict what the [[Count Rate|count rate]] was 2 [[minute]]s before the [[sample]] was first tested.
:Since the '''half life''' is 3 [[minute]]s the [[Count Rate|count rate]] 3 [[minute]]s later can be doubled.
:At 1 minute the [[Count Rate|count rate]] was 3968Bq. Therefore at -2 [[minute]]s the [[Count Rate|count rate]] would have been:
:3968x2= 7936Bq
==Key Stage 4 Higher==
===Meaning===
[[File:HalfLifeGraph1.png|right|300px|thumb|A [[graph]] showing the [[fraction]] of [[Unstable Isotope|unstable isotope]] left compared to the '''half life'''.]]
A '''half life''' is the time it takes for half of the [[Unstable Isotope|unstable isotopes]] in a [[radioactive]] sample to [[Radioactive Decay|decay]].
===About Half Life===
: Every [[isotope]] has a unique '''half life'''.
: The '''half life''' of an [[isotope]] depends on how [[Stable Isotope|stable]] the [[isotope]] is.
: The '''half life''' of an [[isotope]] can be determined by measuring the [[emission]] of [[Ionising Radiation|ionising radiation]]. The time it takes for the [[Count Rate|count rate]] of [[Ionising Radiation|ionising radiation]] to halve, is the same as its '''half life'''.
{| class="wikitable"
|-
|[[File:UnstableIsotopeDecay.png|center|600px]]
|-
| style="height:20px; width:200px; text-align:left;" |This [[diagram]] shows the number of [[Fermium]]-252 [[atom]]s halves each day, so the '''half life''' is 1 day.
|}
: The '''half life''' of an [[isotope]] can be found from plotting a [[graph]] of the amount or [[isotope]] or the [[Count Rate|count rate]] against the [[time]]. The '''half life''' is the time these take to halve from their initial value.
: The [[Count Rate|count rate]] of a sample of [[Unstable Isotope|unstable isotope]] can be predicted given its initial [[Count Rate|count rate]], its '''half life''' and the [[time]] it has been given.
===Finding Half Life from a Graph===
{| class="wikitable"
|-
| style="height:20px; width:300px; text-align:center;" |Find the '''half life''' from this [[graph]].
| style="height:20px; width:300px; text-align:center;" |Find the '''half life''' from this [[graph]].
|-
|[[File:HalfLifeGraph2.png|center|300px]]
|[[File:HalfLifeGraph3.png|center|300px]]
|-
| style="height:20px; width:300px; text-align:center;" |There is 100% of the [[isotope]] at the beginning. Draw a horizontal line from 50% to the curve. Draw a vertical line down from the curve to indicate the '''half life'''.
| style="height:20px; width:300px; text-align:center;" |The [[Count Rate|count rate]] began at 70,000Bq. Draw a horizontal line from 35,000 (half the initial count rate) to the curve. Draw a vertical line down from the curve to indicate the '''half life'''.
|-
|[[File:HalfLifeGraph2b.png|center|300px]]
|[[File:HalfLifeGraph3b.png|center|300px]]
|-
| style="height:20px; width:300px; text-align:center;" |
'''Half Life''' = 4 [[minute]]s
| style="height:20px; width:300px; text-align:center;" |
'''Half Life''' = 6 [[hour]]s
|}
===Equation===
New Count Rate = (Initial Count Rate)/(2<sup>number of '''half lives'''</sup>)
<math>R = \frac{R_I}{2^n}</math>
Where:
<math>R</math> = New [[Count Rate]] or number of [[atom]]s of an [[Unstable Isotope|unstable isotope]] left.
<math>R_I</math> = Initial [[Count Rate]] or number of [[atom]]s of an [[Unstable Isotope|unstable isotope]].
<math>n</math> = The number of '''half lives'''.
===Calculating Count Rate===
{| class="wikitable"
|-
| style="height:20px; width:300px; text-align:center;" |An [[isotope]] has an initial [[Count Rate|count rate]] of 16000Bq and a '''half life''' of 2.5 days. Calculate the [[Count Rate|count rate]] of the [[isotope]] after 17.5 days.
| style="height:20px; width:300px; text-align:center;" |A [[radioactive]] [[sample]] begins with 576 [[atom]]s of an [[Unstable Isotope|unstable isotope]]. Given its '''half life''' is 300 seconds, calculate the number of [[atom]]s remaining after 25 minutes.
|-
| style="height:20px; width:300px; text-align:center;" |'''1. Calculate the number of half lives which have occurred.'''
<math>17.5 \div 2.5 = 7</math>
n = 7 '''half lives'''
| style="height:20px; width:300px; text-align:center;" |'''1. Identify how many times the number of [[Unstable Isotope|unstable]] [[atom]]s has halved.'''
<math>25 \times 60 \div 300 = 5</math>
n = 5 '''half lives'''
|-
| style="height:20px; width:300px; text-align:center;" |'''2. Substitute the numbers into the equation and solve.'''
<math>R = \frac{R_I}{2^n}</math>
<math>R = \frac{16000}{2^7}</math>
<math>R = \frac{16000}{128}</math>
<math>R = 125Bq</math>
| style="height:20px; width:300px; text-align:center;" |'''2. Substitute the numbers into the equation and solve.'''
<math>R = \frac{R_I}{2^n}</math>
<math>R = \frac{576}{2^5}</math>
<math>R = \frac{576}{32}</math>
<math>R = 18atoms</math>
|}