Chapter 2. Radiation 1.Radioactivity 2.Radiation interaction with Matter 3.Radiation Doses and hazard Assessment

1)Overview 2)Types of Radioactive Decay 3)Energetics of Radioactive Decay 4)Characteristics of Radioactive Decay 5)Decay Dynamics 6)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. 40 K

The uranium decay series. 222 Rn 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 Decays transmutations 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 Interesting Items: Spectrum （能谱） of particles Energy in gamma decay Energy in beta decay Energy 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. E i ____________ h v E f ____________ E others _________ 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 dipoleE 1 1Yes5.7e-15 E –3 A –2/3 Magnetic dipoleM 1 1No2.2e-14 E –3 Electric quadrupoleE 2 2No6.7e-9 E –5 A –4/3 Magnetic quadrupoleM 2 2Yes2.6e-8 E –5 A –2/3 Electric octupoleE 3 3Yes1.2e-2 E –7 A –2 Magnetic octupoleM 3 3No4.9e-2 E –7 A –4/3 Electric 2 4 -poleE 4 4No3.4e4 E –9 A –8/3 Magnetic 2 4 -poleM 4 4Yes1.3e5 E –9 A –2 Nature of Gamma Transitions

Gamma Decay Energy and Spectrum Gamma transition of 7 Li

a) Intensities of the peaks are related to the population of the excited state as well as the half life of the transition. E γ 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

Po   particle energy: | 98.9% MeV| 0.5% 9.45 | 0.5% 8.55 | | 207 Pb| 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 Q α 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. ?

c) The mass of the neutrino is negligibly small.

19 d) Positron Decay Energy

1)Overview 2)Types of Radioactive Decay 3)Energetics of Radioactive Decay 4)Characteristics of Radioactive Decay 5)Decay Dynamics 6)Naturally Occurring Radionuclides 2.1 Radioactivity

4) Characteristics of Radioactive Decay 137m Ba decay data,

Stochastic process Radioactivity or decay rate A is the rate of disintegration of nuclei. Initially (at t = 0), we have N o nuclei, and at time t, we have N nuclei. This rate is proportional to N, and the proportional constant is called decay constant. d N A = – ––––– = N Integration gives d t ln N = ln N o – t or N = N o e – t Also A = A o e – t activity or decay rate A decay constant the number of decays or transmutations 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 Decays24 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 N o = A o

25 Half-life and its measurement Be able to apply these equations! N = N o e – t A = A o e – t ln N = ln N o – t ln A = ln A o – t Determine half life, t ½ Ln( N or A ) t ln N 1 – ln N 2 = ––––––––––– t 1 – t 2 t ½ * = 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 f i that the nuclide will decay by the ith mode is λ is the overall decay constant <-How to calculate

What is the probability 64 Cu decays by positron Emission? The decay constants for the three decay modes of this radioisotope are λ β+ = h -1, λ β- = h -1, and λ EC = h -1. The overall decay constant is The probability that an atom of 64 Cu eventually decays by positron emission is

1)Overview 2)Types of Radioactive Decay 3)Energetics of Radioactive Decay 4)Characteristics of Radioactive Decay 5)Decay Dynamics decay transients 6)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) -> N e = Q 0 /λ t -> the equilibrium condition the special case that Q(t) = Q 0 (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 Q 0 s -1 and that there initially are no radionuclides in the sample material. A(0)=0 A(t) = Q o [1-exp(-λt)] A max = Q Q o = Q o [1-exp(-λt)]

b) Three Component Decay Chains

Daughter Decays Faster than the Parentλ I < λ 2, 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 A 2 (t)= A 2 (0)e -λ2t + the daughter decays in accordance with its normal decay rate.

1)Overview 2)Types of Radioactive Decay 3)Energetics of Radioactive Decay 4)Characteristics of Radioactive Decay 5)Decay Dynamics 6)Naturally Occurring Radionuclides 2.1 Radioactivity

6.1 Cosmogenic Radionuclides The most prominent of the cosmogenic radionuclides are tritium 3 H and 14 C. 14 N(n,T) 12 C and 16 O(n,T) 14 N 14 N(n,p) 14 C 12.3 a HTO 5730 a CO 2 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 40 K and 87 Rb since they are inherently part of our body tissue.

Families of Radioactive Decay Series Radioactive Decay Series of 238 U 238 U 92  234 Th  2 (t 1/2 4.5e9 y) 234 Th 90  234 Pa 91 +  – + (t 1/ d) 234 Pa 91  234 U 92 +  – + (t 1/2 6.7 h) 234 U 92 ... (continue) Pb 82 Only alpha decay changes the mass number by 4. There are 4 families of decay series. 4 n, 4 n +1?, 4 n +2, 4 n +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 U radioactive decay series

Radioactivity Np radioactive decay series 2.14 x 10 6 y,

1)Overview 2)Types of Radioactive Decay 3)Energetics of Radioactive Decay 4)Characteristics of Radioactive Decay 5)Decay Dynamics 6)Naturally Occurring Radionuclides 2.1 Radioactivity