Kyoung-Jae Chung
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Introduction to Nuclear Engineering, Fall 2020 Radioactive Decay Fall, 2020 Kyoung-Jae Chung Department of Nuclear Engineering Seoul National University
Transcript of Kyoung-Jae Chung
Introduction to Nuclear Engineering, Fall 2020
Radioactive Decay
Fall, 2020
Kyoung-Jae Chung
Department of Nuclear Engineering
Seoul National University
2 Introduction to Nuclear Engineering, Fall 2020
Activity
Radiation: transportation of mass and energy through space Radioactivity: the process through which nuclei spontaneously emit subatomic
particles Radioactivity was discovered by Henri Becquerel in 1896. The terms radioactivity was suggested by Marie Curie about four years later.
Activity: the number of radioactive decays in a particular time SI unit: becquerel (Bq), 1 decay per second Old unit: curie (Ci), the activity of 1 g of radium-226 The becquerel is a measure only of quantity of radioactive material
1 Ci = 3.7x1010 Bq
Specific activity: the activity per unit mass
Unit conversion
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Exponential decay law (Rutherford and Soddy, 1902)
Radioactive decay is a random process and has been observed to follow Poisson distribution. What this essentially means is that the rate of decay of radioactive nuclei in a large sample depends only on the number of decaying nuclei in the sample:
Activity
ππππ : decay constantβππππππππ
β ππππππππππ
= βππππππ
π΄π΄ = βππππππππ
= ππππππ π΄π΄ = π΄π΄0ππβπππππ‘π‘ = π΄π΄0ππβπ‘π‘/ππ
Half-life ππ1/2 =ln 2ππππ
= 0.693ππππ : decay time
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Mean lifetime
Given an assembly of elements, the number of which decreases ultimately to zero, the mean lifetime, ππ (also called simply the lifetime) is the expected value of the amount of time before an object is removed from the assembly. The mean lifetime is the arithmetic mean of the individual lifetimes.
ππ = ππ = οΏ½0
βππ exp βππππππ ππππππππ =
1ππππ
Expectation
Decay probability between ππ and ππ + ππππ
Probability of surviving until time ππ
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Exponential decay
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Exponential decay
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Specific activity
The specific activity of a sample is defined as its activity per unit mass, for example, Bq gβ1 or Ci gβ1.
Since the number of atoms per gram of the nuclide is ππ = 6.02 Γ 1023/ππ (ππ: atomic weight), the specific activity is given by
πππ΄π΄ =6.02 Γ 1023 ππππ
ππβ
4.17 Γ 1023
π΄π΄ππ1/2
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Serial radioactive decay
We can calculate the activity of a sample in which one radionuclide produces one or more radioactive offspring in a chain.
ππππ2ππππ = ππ1ππ1 β ππ2ππ2 = ππ1ππ10ππβππ1π‘π‘ β ππ2ππ2 ππ
ππππ1ππππ
= βππ1ππ1 ππ1(ππ) = ππ10ππβππ1π‘π‘
ππ1 βΉ ππ2 βΉ ππ3 βΉ β―ππ1 ππ2 ππ3
ππ20 = 0ππ2(ππ) = ππ10
ππ1ππ2 β ππ1
ππβππ1π‘π‘ β ππβππ2π‘π‘
The activity of the daughter nuclei
π΄π΄2 ππ = ππ2ππ2 ππ = ππ2ππ10ππ1
ππ2 β ππ1ππβππ1π‘π‘ β ππβππ2π‘π‘
= π΄π΄1(ππ)ππ2
ππ2 β ππ11 β ππβ(ππ2βππ1)π‘π‘
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Serial radioactive decay
No equilibrium (ππ1 < ππ2): When the daughter, initially absent (ππ20 = 0), has a longer half-life than the parent, its activity builds up to a maximum and then declines. Because of its shorter half life, the parent eventually decays away and only the daughter is left. No equilibrium occurs.
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Serial radioactive decay
Transient equilibrium (ππ1 β³ ππ2)
π΄π΄2 ππ = ππ2ππ2 ππ = π΄π΄1 ππππ2
ππ2 β ππ11 β ππβ ππ2βππ1 π‘π‘ β
ππ2ππ2 β ππ1
π΄π΄1 ππ
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Serial radioactive decay
Secular equilibrium (ππ1 β« ππ2 or ππ2 β« ππ1)
π΄π΄2 ππ = ππ2ππ2 ππ = π΄π΄1 ππππ2
ππ2 β ππ11 β ππβ ππ2βππ1 π‘π‘ β π΄π΄1 ππ 1 β ππβππ2π‘π‘ β π΄π΄1 ππ
π΄π΄1 = π΄π΄10ππβππ1π‘π‘
Total activity ~ 2π΄π΄1
A chain of ππ short-lived radionuclides can all be in secular equilibrium with a long-lived parent. Then the activity of each member of the chain is equal to that of the parent and the total activity is ππ + 1 times the activity of the original parent.
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Bateman equation (1910)
General radioactive chain rule
Initial conditions
Solution
ππ1(0) β 0
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Carbon dating
Formation of radiocarbon
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Radioactive series
Most of the radionuclides found in nature are members of four radioactive series, with each series consisting of a succession of daughter products all ultimately derived from a single parent nuclide.
The reason that there are exactly four series follows from the fact that alpha decay reduces the mass number of a nucleus by 4.
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Radioactive decay of Th-232 and U-238
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Radon and radon daughters
The potential health hazard arises when radon in the air decays, producing nongaseous radioactive daughters. When inhaled, the airborne daughters can be trapped in the respiratory system, where they are likely to decay before being removed by normal lung-clearing mechanisms of the body.
Short-lived alpha emitters
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100
101
102
103
104
105
106
0
10
20
30
40
50
60
70
80
90
100
Rn-222
Po-218
Pb-214
Bi-214
Po-214
Pb-210
Homework
J. Turner, Atoms, Radiation, and Radiation Detection, Wiley (2007), chapter 4Problems: 12, 13
Setup the decay equations and solve them (analytically or numerically). Plot the activities of each nuclide and the total activity versus time (up to 10 days). Initial activity of Rn-222 is 100 Bq and the others are zero.
Stable
10 sec
π΄π΄(ππ)
