Chapter 2. Radiation
1.Radioactivity
2.Radiation interaction with Matter 3.Radiation Doses and hazard Assessment
1) Overview2) Types of Radioactive Decay3) Energetics of Radioactive Decay4) Characteristics of Radioactive Decay5) Decay Dynamics6) Naturally Occurring Radionuclides
2.1 Radioactivity
1) Overview
Radioactive nuclei and their radiations have properties that are the basis of many of the ideas and techniques of atomic and nuclear physics.
40K
The uranium decay series.
222Rn is responsible for higher levels of background radiation in many parts of the world. because it is a gas and can easily seep out of the earth into unfinished basements and then into the house
Radioactivity in Nature
Radon
5
Radioactive Decaystransmutations of nuclides
Radioactivity means the emission of alpha () particles, beta () particles, or gamma photons () etc. from atomic nuclei. The term radioactivity was actually coined by Marie Curie
Radioactive decay is a process by which the nuclei of a nuclide emit , or rays etc.
In the radioactive process, the nuclide undergoes a transmutation, converting to another nuclide.
1) Overview
Conservation of charge
Conservation of the number of nucleons A
Conservation of mass/energy (total energy)
Conservation of linear momentum
Conservation of angular momentum
2) Types of Radioactive Decay
Apparatus similar to that used by Henri Becquerel to determine the magnetic deflection of radioactive decay products. The magnetic field is perpendicular to the direction of motion of the decay products.
The law of conservation of mass and energy covers all reactions. Sum of mass before reaction = Sum of mass after reaction + Q Q = Sum of mass before reaction - Sum of mass after reaction
Energy in Radioactive DecayBefore decay
Recoiling nucleus
Interesting Items:Spectrum (能谱) of particlesEnergy in gamma decayEnergy in beta decayEnergy in alpha decay
3) Energetics of Radioactive Decay
Gamma Decay Energy
Gamma, , rays are electromagnetic radiation emitted from atomic nuclei. The bundles of energy emitted are called photons.
Ei ____________
h v
Ef ____________
Eothers _________
Excited nuclei are called isomers, and de-excitation is called isomeric transition (IT). Energy for photons
h v = E i - E f
a)
Types of Isomeric Transitions and their Ranges of Half-life
Radiation Type Symbol J Partial half life t (s)
Electric dipole E1 1 Yes 5.7e-15 E–3 A–
2/3
Magnetic dipole M1 1 No 2.2e-14 E–3 Electric quadrupole E2 2 No 6.7e-9 E–5 A–
4/3
Magnetic quadrupole M2 2 Yes 2.6e-8 E–5 A–
2/3
Electric octupole E3 3 Yes 1.2e-2 E–7 A–2
Magnetic octupole M3 3 No 4.9e-2 E–7 A–
4/3
Electric 24-pole E4 4 No 3.4e4 E–9 A–8/3
Magnetic 24-pole M4 4 Yes 1.3e5 E–9 A–2
Nature of Gamma Transitions
Various Gamma Transitions in 7Li
3/ 2– ground state½ – 0.778 MeV
7/ 2+ 4.64 MeV
½+ 6.54 MeV
M1
E1
E3
M3
M2
Gamma Decay Energy and Spectrum
Gamma transition of 7Li
Gamma Ray Spectrum of O18
E
Intensity 2h+2+0+
3.27 MeV
1.981.98 MeV
3.27 MeV
5.25 MeV
a)
Intensities of the peaks are related to the population of the excited state as well as the half life of the transition.
Eγ is the energy of the gamma photon, E* is the excitation energy (above the ground state) of the initial parent nucleus, and Ep is the recoil kinetic energy of the resulting ground-state nuclide.
the kinetic energy of the recoil nucleus is negligible
=Q
15
An Ideal Alpha Spectrum
MeV
No.of
8 10
211Po particle energy: | 98.9% 10.02 MeV | 0.5% 9.45 | 0.5% 8.55 |
| 207Pb |7/2+ 0.90 MeV – 0.5%5/2+ 0.57 MeV – 0.5%1/2+ –
98.9%
b)How is alpha energy evaluated and determined? What is a typical alpha spectrum and why?
Expeimentally?
What is the initial kinetic energy of the alpha particle produced in the radioactive decay:
The Qα value in mass units
17
c) Beta Decay Spectra and Neutrino
Pauli: Neutrino with spin 1/2 is emitted simultaneously with beta, carrying the missing energy.
A Typical Beta SpectrumIntensityor # of
Energy of
E max
A Beta Decay Scheme
PZ DZ+1 + – + v
?
c)
The mass of the neutrino is negligibly small.
19
d) Positron Decay Energy
Positron Emission
+
–
1) Overview2) Types of Radioactive Decay3) Energetics of Radioactive Decay4) Characteristics of Radioactive Decay5) Decay Dynamics6) Naturally Occurring Radionuclides
2.1 Radioactivity
4) Characteristics of Radioactive Decay
137mBa decay data,
Stochastic process
Radioactivity or decay rate A is the rate of disintegration of nuclei. Initially (at t = 0), we have No nuclei, and at time t, we have N nuclei. This rate is proportional to N, and the proportional constant is called decay constant .
dNA = – ––––– = N Integration gives
d t
ln N = ln No – t or N = No e – t
Also A = Ao e – t
activity or decay rate A decay constant
the number of decays ortransmutations per unit of time
specific activity
normalized to the mass or volume of the sample
Many safety limits and regulations are based on the specific activity concept
Radioactive Decays 24
Variation of N as a function of time t
N No
t
N = No e - t
Also A = Ao e - t
Radioactive Decay Kinetics -exponential
Number of radioactive nuclei decrease exponentially with time as indicated by the graph here.
As a result, the radioactivity vary in the same manner.
Note N = A
No = Ao
25
Half-life and its measurementVariation of N as a function of time t
N No
t
N = No e - t
Also A = Ao e - t
Be able to apply these equations!
N = No e– t
A = Ao e – t
ln N = ln No – t ln A = ln Ao – t
Determine half life, t½
Ln(N or A)
t
ln N1 – ln N2
= ––––––––––– t1 – t2
t½ * = ln 2
Half life is not affected by chemical and physical state of matter.
Condition?Very long?
Decay Probability for a Finite Time Interval
does not decay
does decay
As the time interval becomes very small, i.e., t —>Δt « 1,
p(t)dt, probability a radionuclide, which exists at time t = 0, decays in the time interval between t and t + dt
the probability distribution function for when a radionuclide decays.
Mean Lifetime
calculate the average lifetime of a radionuclide by using the decay probability distribution
Ln A
t
Decay by competing Processes
The probability fi that the nuclide will decay by the ith mode is
λ is the overall decay constant
<-How to calculate
What is the probability 64Cu decays by positron Emission? The decay constants for the three decay modes of this radioisotope are λ β+ = 0.009497 h-1, λ β- = 0.02129 h-1, and λ EC = 0.02380 h-1.
The overall decay constant is
The probability that an atom of 64Cu eventually decays by positron emission is
1) Overview2) Types of Radioactive Decay3) Energetics of Radioactive Decay4) Characteristics of Radioactive Decay5) Decay Dynamics decay transients6) Naturally Occurring Radionuclides
2.1 Radioactivity
a) Decay with Production
Q(t) is the rate at which the radionuclide of interest is being created
N(t) -> Ne = Q0/λ t -> the equilibrium condition
the special case that Q(t) = Q0
(a constant production rate)
means?
Example How long after a sample is placed in a reactor is it before the sample activity reaches 75% of the maximum activity? Assume the production of a single radionuclide species at a constant rate of Q0 s-1 and that there initially are no radionuclides in the sample material.
A(0)=0A(t) = Qo[1-exp(-λt)] Amax = Q0
0.75Qo = Qo[1-exp(-λt)]
b) Three Component Decay Chains
Daughter Decays Faster than the Parent λI < λ2,
transient equilibrium: daughter's decay rate is limited by the decay rate of the parent.
λI << λ2,
The activity of the daughter approaches that of the parent. This extreme case is known as secular equilibrium( 久期平衡 ).
Daughter Decays Slower than the Parent
A2(t)= A2(0)e-λ2t +
A2(t)= A2(0)e-λ2t +
the daughter decays in accordance with its normal decay rate.
1) Overview2) Types of Radioactive Decay3) Energetics of Radioactive Decay4) Characteristics of Radioactive Decay5) Decay Dynamics6) Naturally Occurring Radionuclides
2.1 Radioactivity
6.1 Cosmogenic Radionuclides
The most prominent of the cosmogenic radionuclides are tritium 3H and 14C.
14N(n,T)12C and 16O(n,T)14N
14N(n,p)14C
12.3 a HTO
5730 a CO2
electron?
6.2 Singly Occurring Primordial ( 原生) Radionuclides
The solar system was formed about 5 billion years ago. These radionuclides are seen to all have half-lives greater than the age of the solar system. Of these radionuclides, the most significant are 40K and 87Rb since they are inherently part of our body tissue.
Families of Radioactive Decay Series
Radioactive Decay Series of 238U238U92 234Th90 + 42 (t1/2 4.5e9 y)
234Th90 234Pa91 + – + (t1/2 24.1 d)
234Pa91 234U92 + – + (t1/2
6.7 h) 234U92 . . . (continue)
. . .206Pb82
Only alpha decay changes the mass number by 4.
There are 4 families of decay series.4n, 4n+1?, 4n+2, 4n+3,
n being an integer.
Each naturally occurring radioactive nuclide with Z > 83 is a member of one ofthree long decay chains,
thorium (4n), uranium (4n + 2), and actinium (4n + 3)
The Decay Path of 4n + 2 or 238U Family 238U234U234Pa
234Th230Th226Ra
222Rn 218At
218Po214Po214Bi
214Pb
210Po 210Bi206Pb 210Pb 206Tl 210Tl 206Hg
Minor route
Major route
decay
decay
Radioactivity - 238U radioactive decay series
Radioactivity - 239Np radioactive decay series
The Decay Paths of the 4n + 1 or 237Np93 Family Series237Np93
233U92 (2e6 y)(1.6e5 y) 233Pa91
229Th90
225Ac89 (7300 y; minor path) (10 d) 225Ra88
221Fr87
217At85
213Po84 (1 min) 209Bi83 213Bi83
209Pb82
209Tl81
2.14 x 106 y,
1) Overview2) Types of Radioactive Decay3) Energetics of Radioactive Decay4) Characteristics of Radioactive Decay5) Decay Dynamics6) Naturally Occurring Radionuclides
2.1 Radioactivity