Chapter 2. Radiation

Chapter 2. Radiation • Radioactivity 2.Radiation interaction with Matter 3.Radiation Doses and hazard Assessment

2.1 Radioactivity • Overview • Types of Radioactive Decay • Energetics of Radioactive Decay • Characteristics of Radioactive Decay • Decay Dynamics • Naturally Occurring Radionuclides

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

Radioactivity in Nature 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 Radon The uranium decay series.

Overview 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.

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.

3) Energetics of Radioactive Decay 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 Interesting Items: Spectrum（能谱）of particlesEnergy in gamma decayEnergy in beta decayEnergy in alpha decay

a) Gamma Decay Energy Gamma, g, rays are electromagnetic radiation emitted from atomic nuclei. The bundles of energy emitted are called photons. Excited nuclei are called isomers, and de-excitation is called isomeric transition (IT). Energy for photons h v = Ei - E f Ei ____________ h v Ef ____________ Eothers _________

Nature of Gamma Transitions Types of Isomeric Transitions and their Ranges of Half-life Radiation TypeSymbolJPartial half life t (s) Electric dipole E1 1 Yes 5.7e-15 E–3A–2/3Magnetic dipole M1 1 No 2.2e-14E–3 Electric quadrupole E2 2 No 6.7e-9E–5A–4/3Magnetic quadrupole M2 2 Yes 2.6e-8E–5A–2/3 Electric octupole E3 3 Yes 1.2e-2 E–7A–2Magnetic octupole M3 3 No 4.9e-2E–7A–4/3 Electric 24-pole E4 4 No 3.4e4 E–9A–8/3Magnetic 24-pole M4 4 Yes 1.3e5E–9A–2

Gamma Decay Energy and Spectrum Gamma transition of 7Li

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. a) =Q Intensities of the peaks are related to the population of the excited state as well as the half life of the transition. the kinetic energy of the recoil nucleus is negligible

b) How is alpha energy evaluated and determined? What is a typical alpha spectrum and why? 211Poa 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% Expeimentally?

What is the initial kinetic energy of the alpha particle produced in the radioactive decay: The Qα value in mass units

c) Beta Decay Spectra and Neutrino ? Pauli: Neutrino with spin 1/2 is emitted simultaneously with beta, carrying the missing energy.

c) The mass of the neutrino is negligibly small.

d) Positron Decay Energy

4) Characteristics of Radioactive Decay 137mBa decay data,

activity ordecay rateA decay constant  Radioactivity or decay rateA 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 lnN = lnNo – t or N = No e– t the number of decays or transmutations per unit of time Also A = Ao e– t Stochastic process

specific activity normalized to the mass or volume of the sample Many safety limits and regulations are based on the specific activity concept

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 lN = A lNo = Ao Radioactive Decays

Condition? Very long? Half-life and its measurement Ln(N or A) lnN1 – lnN2  = –––––––––––t1 – t2 t½*  = ln 2 Be able to apply these equations! N = Noe– tA = Aoe – t lnN = lnNo – t lnA = lnAo – t Determine half life, t½ t Half life is not affected by chemical and physical state of matter.

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

Decay by competing Processes Ln A t λ is the overall decay constant The probability fi that the nuclide will decay by the ith mode is <-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

2.1 Radioactivity • Overview • Types of Radioactive Decay • Energetics of Radioactive Decay • Characteristics of Radioactive Decay • Decay Dynamics decay transients • Naturally Occurring Radionuclides

a) Decay with Production Q(t) is the rate at which the radionuclide of interest is being created the special case that Q(t) = Q0 (a constant production rate) N(t) -> Ne= Q0/λ t -> the equilibrium condition • 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(t) = Qo[1-exp(-λt)] A(0)=0 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 theparent. • 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.

6.1 CosmogenicRadionuclides The most prominent of the cosmogenicradionuclides are tritium 3H and 14C. 14N(n,T)12C and 16O(n,T)14N 12.3 a HTO 14N(n,p)14C 5730 a CO2 electron?

6.2 Singly Occurring Primordial(原生）Radionuclides The solar system was formed about 5billion years ago. These radionuclides are seen to all have half-lives greater than the age of the solar system. Of these radionuclides, the mostsignificant are 40K and 87Rb since they are inherently part of our body tissue.

Families of Radioactive Decay Series Radioactive Decay Series of 238U 238U92®234Th90 + 4a2 (t1/2 4.5e9 y) 234Th90®234Pa91 + b– + n (t1/2 24.1 d) 234Pa91®234U92 + b– + n (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 of three long decay chains, thorium (4n), uranium (4n + 2), and actinium (4n + 3)

Radioactivity - 238U radioactive decay series

Radioactivity - 239Np radioactive decay series 2.14 x 106 y,

Chapter 2. Radiation