Half Life

Half Life

Half Life is the time for the activity to halve.

Time for activity to (decrease by) half
or  time for half the nuclei to decay

 (It is measured in units of time, e.g seconds, minutes, days, years, millions of years!)

Note the SQA do NOT accept: Time for radiation/radioactivity/ count rate to half

half-life-tablehalf-life-formula

From the Yellow Chemcord Book- this is how to answer the questions HALF LIFE QUESTIONS

Chemcord have kindly giving permission to upload these questions here. If you thought they were useful you can buy the National 5 Revision books soon:

Chemcord Sample N5

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half life Questions A print out for those who would like a copy of the National 5 Chemcord revision questions on half life. Here are the questions written out: HALF LIFE QUESTIONS

  1. What is meant by the half life of a radioactive substance?
  2. The activity of a source drops from 1000 kBq to 125 kBq in 9 days. Calculate the half life of the source.
  3. The activity of a source drops from 4800 kBq to 150 kBq in 10 days. Calculate the half life of the source.
  4. The activity of a source drops from 720 MBq to 45 MBq in 20 years. Calculate the half life of the source.
  5. The activity of a source drops from 4096 kBq to 1 kBq in 2 days. Calculate the half life of the source.
  6. The activity of a source drops from 448 kBq to 3.5 kBq in 17.5 years. Calculate the half life of the source.
  7. A source has an activity of 1800 kBq and a half life of 2 days. What is its activity 10 days later?
  8. A source has an activity of 576 MBq and a half life of 30 years. What is its activity 180 years later?
  9. A source has an activity of 2400 kBq and a half life of 8 s. What is its activity 32 s later?
  10. A source has an activity of 3200 kBq and a half life of 5.3 days. What is its activity 37.1 days later?
  11. A source has an activity of 800 kBq after being stored for 4 days. If the half life is 1 day, what was its initial activity?
  12. A source has an activity of 1800 kBq after being stored for 72 s. If the half life is 24 s, what was its initial activity?
  13. A source has an activity of 40 kBq after being stored for 10 years. If the half life is 2 years, what was its initial activity?
  14. A source has an activity of 30 kBq after being stored for 2 days. If the half life is 8 h, what was its initial activity?
  15. A source has an activity of 40 MBq and a half life of 15 s. How long will it take for its activity to drop to 625 kBq?
  16. A source has an activity of 25 MBq and a half life of 8 days. Approximately how long will it take for its activity to drop to below 1MBq?
  17. A source has an activity of 320 MBq and a half life of 1000 years. Approximately how long will it take for its activity to drop to 500 kBq?
  18. A background count rate of 20 counts per minute is measured in the absence’ of a source. When the source is present the count is 140 counts per minute initially, dropping to 35 counts per minute after 15 days. What is the half life to of the source?
  19. If the background count is 28 counts per minute and the count with a source drops from 932 to 141 counts per minute in 24 h, what is the half life of the source?
  20. If the background count rate is 24 counts per minute and the count rate with a source present drops from 4120 to 25 counts per minute in 2 days, what is the half life of the source?
  21. In an experiment with a radioactive source, the count rate corrected for background radiation was measured and the following results obtained.
Time

in minutes

Corrected

Count Rate

in c.p.m.

0

1

2

3

4

5

100

58

32

18

10

5.6

a) Plot a graph to show these results.

b) Estimate the half life of the source from these results.

22. In an experiment with a source, carried out in an area where there is a high background radiation, the following results were obtained.

Time (s) Count Rate 

(c.p.m.)

0

30

60

90

120

150

180

210

240

270

300

88

72

60

52

44

39

36

34

32

29

30

              

a) Plot a graph to show these results.

b) Estimate the background count rate.

c) Estimate the half life of the source from these results.

ANSWERS

  1. time taken for the activity to decrease by half
  2. 3 days
  3. 2 days
  4. 5 years
  5. 4h
  6. 2.5 years
  7. 56.25kBq
  8. 9 MBq
  9. l50 kBq
  10. 25 kBq
  11. 12.8 MBq
  12. 14.4 MBq
  13. 1.28 MBq
  14. 1920 kBq
  15. 90s
  16. 32 to 40days
  17. 9500 years
  18. 5 days
  19. 8 h
  20. 73.   4h

For Questions 2-6 (to find t ½ when Ao and A known)

Step

  1. Summarise
  2. Starting with the original activity keep halving until you reach the final activity
  3. COUNT THE ARROWS. This is the NUMBER of half lives.
  4. Use the formula    t½= time÷No. of t ½
  5. Don’t forget to write out the time.

 For Questions 7-10 (to find the final activity when t and t ½  are known)  Step

  1. Summarise
  2. Use the formula to find the number of half lives (this will be the number of arrows) No. of t ½ = time÷ t½
  3. Starting with the original activity keep halving until you reach the final activity
  4. COUNT THE ARROWS. This is the NUMBER of half lives.
  5. Don’t forget to write out the units for final activity.

For Questions 11-14 (to find Ao when A, t ½ and time are known)

Steps

  1. Summarise
  2. Use the formula to find the number of half lives (this will be the number of arrows)   No. of t ½ = time÷ t½
  3. DOUBLE the final activity for the number of t ½ eg If you have 4 half lives double the final activity 4 times. NB DO NOT MULTIPLY BY 4
  • The alternative is to MULTIPLY the final activity by 2n (2 to the power n where n is the number of half lives)
  • The number at the end of the arrows is your original activity, don’t forget to add the units.

For Questions 15-17

Step

  1. Summarise
  2. Starting with the original activity keep halving until you reach the final activity
  3. Count the Arrows
  4. Use the formula     time = t½ × No. of t ½

Experiment to Measure Half Life

The activity of a radioactive source decreases time. However the rate of decrease slows with time. Because of this, and because the decay of individual atoms is random and unpredictable, theoretically a radioactive source will never completely lose all of its activity. The time taken for half of the atoms in a radioactive sample to decay is a constant for that source called the half-life of the source. So the half-life of a radioactive source is the time period during which the activity of the source falls to half of its original value. The half-life of some sources is as low as a fraction of a second; for others it is many thousands of years.

Finding the half-life of a radioactive source

Apparatus: Geiger-Muller tube, Scaler counter or ratemeter, Source (eg.sealed protactinium-234 radioactive source and drip tray).

 half-life-exptInstructions:

  • Use the Geiger-Muller tube and scaler counter to measure the back­ground count rate.
  • Record this value.
  • Set up the apparatus shown in the diagram.
  • Measure and record values of count rate and time interval for a suit­able time period.
  • Correct all your measurements for background by taking the background count off all other measured count rates..
  • Plot a graph of COUNT RATE or ACTIVITY against TIME.
  • Find the half life from the graph

half-life-graph

Half life and safety

To measure the half-life of a radioactive source, the level of the background radiation is first measured. Then the count rate with the radioactive source present is measured over a suitable period of time using a suitable detector such as a Geiger-Muller tube connected to a scaler. A graph of the count rate (with the source present), corrected for background radiation, is plotted.A suitable count rate value is chosen, say 80 counts per minute, and the time at which the source had this count rate, t1, is marked as above. In a similar way the time t2 at which the count rate is half the previous value, 40 counts per minute, is found. The half-life of the source is the time period t2 -t1. Any starting value can be chosen, the time period for the count rate to halve in value will always be the same.

EXAMPLE

In six years, the activity of a radioactive isotope drops from 200 kBq to 25kBq. Calculate the half-life of the isotope.

SOLUTION: original activity = 200 kBq 

Activity after 1 half-life = ½ ×200 kBq = 100 kBq

Activity after 2 half-lives = ½ × 100 kBq = 50 kBq

Activity after 3 half-lives = ½ × 50kBq = 25 kBq

 

So 6 years represents 3 half-lives, thus one half-life is 2 years.

Safety with radiation

There are several safety precautions that must be taken when handling radioactive substances.

  • Always handle radioactive substances with forceps. Do not use bare hands.
  • Never point radioactive substances at anyone.
  • Never bring radioactive substances close to your face, particularly your eyes.
  • Wash hands thoroughly after using radioactive substances especially after using open sources or radioactive rock samples.
  • Unauthorised people must not be allowed to handle radioactive substances. In particular, in the United Kingdom, no one under 16 years of age may handle radioactive substances.

In addition there are several safety precautions relating to the storage and monitoring of radioactive substances.

  • Always store radioactive substances in suitable lead-lined containers.
  • As soon as source has been used, return it to its safe storage container, to avoid unnecessary contamination.
  • Keep a record of the use of all radioactive sources.

The equivalent dose received by people can be reduced by three methods:

  • shielding;
  • limiting the time of exposure;
  • increasing the distance from the source.

Stay safe and keep under your annual dose of 2.2 mSv!

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Half life Results- Protactinium-234 and Indium-116

Here are the results from the Protactinium Generator Experiment. Your task is to correct for background (take the background count per second away from the count rate) and then plot a graph of count rate (cps) against time (s). Remember the count rate was taken every 10 s but shows the value of the count rate (for one second)

Background count rate (c.p.m.) 48.0,   46.0,   42.0

Average background count rate (c.p.m.)    45.3

Average background per second (c.p.s.)    work it out!

TimeCount rate
(s)(cps)
080.3
1073.9
2067.3
3060.5
4055.2
5049.6
6045.7
7041.5
8037.4
9034.1
10031.3
11028.5
12025.9
13023.9
14021.7
15019.4
16017.6
17016
18014.9
19013.4
20012.3
21011.2
22010.2
2309.2
2408.4
2507.5
2606.9
2706.4
2805.7
2905.3
3004.7

Pa-234-graph

Indium 116 Half Life

Here are the results for the Indium-116 half life experiment. Warning, do not plot a graph in 15 minute intervals or you will have more difficulty finding the half life. Make the scale ten minute intervals.

You can track the experiment yourself through the link below

Indium-116 files

Background count = 31 c.p.m.

Time Time from startCount rate
(hours)(mins)(c.p.s.)
9:000675
9:1515570
9:3030452
9:4545375
10:0060328
10:1575275
10:3090219
10:45105181
11:00120164
11:15135149
11:30150126
11:45165106
12:0018090

in-116-graph

 

Here are three more examples for you to practice producing a half life graph and for finding the half life of Protactinium

Example 1:

Background Count (cps):    5,   5,   3,  5,   4,   5,   5.

Time (s)Count in 10s
0308
10279
20240
30217
40197
50182
60165
70158
80145
90129
100116
110109
12098
13089
14080
15075
16066
17060
18055
19050
20046
21043
22035
Example 2:

Background Count (cps):     4,       3,      5.

Time (s)Count in 10s
0841
10752
20693
30622
40593
50544
60481
70443
80392
90364
100341
110301
120272
130251
140243
150211
160204
170183
180172
Example 3:
time
(s)
Count
in 10s
corrected
count
in 10s
Corrected
Count
Rate
(cps)
Background
count
(cp10s)
0
5105100.510.055
209590.59.055
358176.57.653
509085.58.555
658681.58.154.5
807368.56.85
957671.57.15
1107974.57.45
1255348.54.85
1405348.54.85
1555853.55.35
1706156.55.65
1856055.55.55
2004338.53.85
2156055.55.55
2304843.54.35
2454540.54.05
2604439.53.95
2754237.53.75
2904742.54.25
3052823.52.35
3203126.52.65
3353631.53.15
3503227.52.75
3652419.51.95

You should now have had plenty of practice at finding the half life graphically, nothing should phase you now.

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