Section 18.3 Radioactive Decay
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Section 18.3 Radioactive decay • • • • © Manhattan Press (H.K.) Ltd.
The cause of radioactivity Random nature of decay Decay curve Half-life 1
18.3 Radioactive decay (SB p. 20)
The cause of radioactivity proton
neutron
strong attractive nuclear force For stable nucleus
proton
proton
electrostatic repulsion
© Manhattan Press (H.K.) Ltd.
2
18.3 Radioactive decay (SB p. 21)
The cause of radioactivity For a stable nucleus, N N (neutron no.) 1 ≤ ≤1.5 Z (proton no.) Z Otherwise, nucleus → unstable → breaks up → emits radiation → stable Radioactive decay occurs in unstable nuclides © Manhattan Press (H.K.) Ltd.
3
18.3 Radioactive decay (SB p. 21)
Random nature of decay activity
— no. of disintegrations / s
1 Becquerel (Bq) = 1 disintegration per second
© Manhattan Press (H.K.) Ltd.
4
18.3 Radioactive decay (SB p. 21)
Throwing a dice Decay process similar to throwing a dice
probability of getting any one face = 1/6 © Manhattan Press (H.K.) Ltd.
5
18.3 Radioactive decay (SB p. 22)
Dice decay analogue Expt 18D Dice decay analogue undecayed nucleus decayed nucleus
© Manhattan Press (H.K.) Ltd.
6
18.3 Radioactive decay (SB p. 22)
Dice decay analogue Radioactive decay — random process
? n e h W Wh ic h
?
unpredic table
activity ∝ no. of undecayed nuclei © Manhattan Press (H.K.) Ltd.
7
18.3 Radioactive decay (SB p. 23)
Decay curve decay curve count rate: no. of counts recorded / s corrected count rate: measured count rate − background count rate
© Manhattan Press (H.K.) Ltd.
8
18.3 Radioactive decay (SB p. 23)
Decay curve A typical decay curve Time / s
0
10
20
30
40
Corrected count rate / s−1 800 400 200 100 50
corrected count rate falls exponentially with time
© Manhattan Press (H.K.) Ltd.
9
18.3 Radioactive decay (SB p. 23)
Half-life half-life — time for half the sample nuclei decay e.g., half-life of randon = 3.8 days
2 000 000 / 2
© Manhattan Press (H.K.) Ltd.
1 000 000 / 2
500 000 / 2
10
18.3 Radioactive decay (SB p. 24)
Half-life
CAL Workshop 2 Decay curve and half-life © Manhattan Press (H.K.) Ltd.
11
18.3 Radioactive decay (SB p. 24)
Half-life shorter half-life → decays faster
© Manhattan Press (H.K.) Ltd.
12
18.3 Radioactive decay (SB p. 25)
Example 4: The following graph shows the decay curve of protactinium-234.
(a) What is the background count rate? The background count rate is 2 counts per second. © Manhattan Press (H.K.) Ltd.
Solut ion 13
18.3 Radioactive decay (SB p. 25)
Example 4: (Cont)
Solut (b) Determine the half-life of protactinium-234. ion The graph of corrected count rate against time is shown below.
From the graph, the half-life of protactinium-234 is about 56 s. © Manhattan Press (H.K.) Ltd.
14
18.3 Radioactive decay (SB p. 26)
Half-life Half-lives of some typical radioactive substances Radioactive substance Polonium-214 Radon-222 Cobalt-60 Radium-226 Carbon-14 Uranium-238
© Manhattan Press (H.K.) Ltd.
Half-life 0.000 164 second 3.82 days 5.3 years 1 600 years 5 600 years 4.5 × 109 years
15
18.3 Radioactive decay (SB p. 26)
Half-life Are the radioactive substances hazardous Larger sample more dangerous • short half-lives have high initial count rates • very long half-lives not very radioactive BUT prolonged effect
© Manhattan Press (H.K.) Ltd.
16
18.3 Radioactive decay (SB p. 26)
Class Practice 4: A student uses a GM counter to measure the radiation emitted by actinium-228 nuclei. He does so by recording the count rate of actinium-228 at every 30-minute interval. The background count rate is found to be 5 counts per second. The following table shows the results.
Time / min
0
Count rate / count s−1
410 299 215 160 125 90
© Manhattan Press (H.K.) Ltd.
30
60
90
120 150
17
18.3 Radioactive decay (SB p. 27)
Class Practice 4: (Cont) (a) Complete the following table.
Time / min
0
Corrected count rate / count s−1
405
© Manhattan Press (H.K.) Ltd.
Ans wer
30
60
294 210
90
120 150
155 120
85
18
18.3 Radioactive decay (SB p. 27)
Class Practice 4: (Cont) (b) Plot a graph showing the corrected count rate due to actinium-228 against time. Determine the half-life of actinium-228. Ans wer From the graph, the half-life of actinium-228 is ____________ minutes. 65 Ans wer
© Manhattan Press (H.K.) Ltd.
19
18.3 Radioactive decay (SB p. 27)
Class Practice 4: (Cont) (c) Explain briefly why not all the points lie on the decay curve. Ans wer Since radioactive decay is a random process, there are fluctuations in the number of decayed nuclei. Thus, not all the points lie on the decay curve.
© Manhattan Press (H.K.) Ltd.
20
To section 18.4
© Manhattan Press (H.K.) Ltd.
21
The cause of radioactivity Random nature of decay Decay curve Half-life 1
18.3 Radioactive decay (SB p. 20)
The cause of radioactivity proton
neutron
strong attractive nuclear force For stable nucleus
proton
proton
electrostatic repulsion
© Manhattan Press (H.K.) Ltd.
2
18.3 Radioactive decay (SB p. 21)
The cause of radioactivity For a stable nucleus, N N (neutron no.) 1 ≤ ≤1.5 Z (proton no.) Z Otherwise, nucleus → unstable → breaks up → emits radiation → stable Radioactive decay occurs in unstable nuclides © Manhattan Press (H.K.) Ltd.
3
18.3 Radioactive decay (SB p. 21)
Random nature of decay activity
— no. of disintegrations / s
1 Becquerel (Bq) = 1 disintegration per second
© Manhattan Press (H.K.) Ltd.
4
18.3 Radioactive decay (SB p. 21)
Throwing a dice Decay process similar to throwing a dice
probability of getting any one face = 1/6 © Manhattan Press (H.K.) Ltd.
5
18.3 Radioactive decay (SB p. 22)
Dice decay analogue Expt 18D Dice decay analogue undecayed nucleus decayed nucleus
© Manhattan Press (H.K.) Ltd.
6
18.3 Radioactive decay (SB p. 22)
Dice decay analogue Radioactive decay — random process
? n e h W Wh ic h
?
unpredic table
activity ∝ no. of undecayed nuclei © Manhattan Press (H.K.) Ltd.
7
18.3 Radioactive decay (SB p. 23)
Decay curve decay curve count rate: no. of counts recorded / s corrected count rate: measured count rate − background count rate
© Manhattan Press (H.K.) Ltd.
8
18.3 Radioactive decay (SB p. 23)
Decay curve A typical decay curve Time / s
0
10
20
30
40
Corrected count rate / s−1 800 400 200 100 50
corrected count rate falls exponentially with time
© Manhattan Press (H.K.) Ltd.
9
18.3 Radioactive decay (SB p. 23)
Half-life half-life — time for half the sample nuclei decay e.g., half-life of randon = 3.8 days
2 000 000 / 2
© Manhattan Press (H.K.) Ltd.
1 000 000 / 2
500 000 / 2
10
18.3 Radioactive decay (SB p. 24)
Half-life
CAL Workshop 2 Decay curve and half-life © Manhattan Press (H.K.) Ltd.
11
18.3 Radioactive decay (SB p. 24)
Half-life shorter half-life → decays faster
© Manhattan Press (H.K.) Ltd.
12
18.3 Radioactive decay (SB p. 25)
Example 4: The following graph shows the decay curve of protactinium-234.
(a) What is the background count rate? The background count rate is 2 counts per second. © Manhattan Press (H.K.) Ltd.
Solut ion 13
18.3 Radioactive decay (SB p. 25)
Example 4: (Cont)
Solut (b) Determine the half-life of protactinium-234. ion The graph of corrected count rate against time is shown below.
From the graph, the half-life of protactinium-234 is about 56 s. © Manhattan Press (H.K.) Ltd.
14
18.3 Radioactive decay (SB p. 26)
Half-life Half-lives of some typical radioactive substances Radioactive substance Polonium-214 Radon-222 Cobalt-60 Radium-226 Carbon-14 Uranium-238
© Manhattan Press (H.K.) Ltd.
Half-life 0.000 164 second 3.82 days 5.3 years 1 600 years 5 600 years 4.5 × 109 years
15
18.3 Radioactive decay (SB p. 26)
Half-life Are the radioactive substances hazardous Larger sample more dangerous • short half-lives have high initial count rates • very long half-lives not very radioactive BUT prolonged effect
© Manhattan Press (H.K.) Ltd.
16
18.3 Radioactive decay (SB p. 26)
Class Practice 4: A student uses a GM counter to measure the radiation emitted by actinium-228 nuclei. He does so by recording the count rate of actinium-228 at every 30-minute interval. The background count rate is found to be 5 counts per second. The following table shows the results.
Time / min
0
Count rate / count s−1
410 299 215 160 125 90
© Manhattan Press (H.K.) Ltd.
30
60
90
120 150
17
18.3 Radioactive decay (SB p. 27)
Class Practice 4: (Cont) (a) Complete the following table.
Time / min
0
Corrected count rate / count s−1
405
© Manhattan Press (H.K.) Ltd.
Ans wer
30
60
294 210
90
120 150
155 120
85
18
18.3 Radioactive decay (SB p. 27)
Class Practice 4: (Cont) (b) Plot a graph showing the corrected count rate due to actinium-228 against time. Determine the half-life of actinium-228. Ans wer From the graph, the half-life of actinium-228 is ____________ minutes. 65 Ans wer
© Manhattan Press (H.K.) Ltd.
19
18.3 Radioactive decay (SB p. 27)
Class Practice 4: (Cont) (c) Explain briefly why not all the points lie on the decay curve. Ans wer Since radioactive decay is a random process, there are fluctuations in the number of decayed nuclei. Thus, not all the points lie on the decay curve.
© Manhattan Press (H.K.) Ltd.
20
To section 18.4
© Manhattan Press (H.K.) Ltd.
21
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