Nuclear Spectroscopy: Radioactivity and Half Life

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1 Particle and Spectroscopy: and Half Life 02/08/2018 My Office Hours: Thursday 1:00-3:00 PM 212 Keen Building

2 Outline

3 Some nuclei are unstable and decay spontaneously into two or more particles. This process is called radioactive decay. The term radioactivity refers to the process in which a nucleus spontaneously emits either particles or radiation. When a nucleus decays, it can emit particles or photons: The radioactive decay products were originally called alpha (α), beta (β) and gamma (γ). Generally, all are called radiation even though only gamma is actually a form of electromagnetic radiation.

4 : α Decay An α particle is composed of two protons and two neutrons: This is a He nucleus and is denoted as 4 2 He. The α particle does not carry any electrons: Q = +2e. Example: Ra Rn He (The number of nucleons is conserved.)

5 There are two varieties of β particles: : The negatively-charged particle is an electron. The positively-charged particle is a positron. (same mass as electron; both are point charges.) Example: 14 6 C 14 7 N + e + ν

6 : γ Decay The excited nucleus can emit γ rays with different energies: This depends on which excited and final states are involved. Typical gamma rays have energies from about 10 kev to 100 MeV or higher. γ rays versus X-rays: γ rays are produced in nuclear reactions. X-rays are generated by atomic electrons.

7 : γ Decay Typical lifetimes of nuclear levels decaying by photon emission are about s. Role of angular momentum in γ decays also crucial: J = S i S f with S i + S f J S i S f m i = M + m f magnetic quantum number

8 : Fission A Z X A Z B + A A Z Z C Spontaneous Fission when spherical nucleus deforms Famous example: U La + 35Br + 3n releases about 154 MeV in kinetic energy surface Coulomb determines stability

9 : Fission Induced Fission: A Z X A Z B + A A Z Z C 235 U + n slow 236 U MeV binding energy 238 U + n fast (fission barrier is 5 MeV)

10 s α β A Z X A 4 Z 2 Y He A Z X A Z 1 Y + e+ + ν e A Z X A Z +1 Y + e + ν e A Z X + e A Z 1 Y + ν e γ A Z X A Z Y + γ General rules: Excited nucleus γ decay Near stability β decay Far from stability α decay or fission

11 Conservation Rules All radioactive decays obey certain conservation rules: 1 Conservation of mass-energy: The total energy at the start of the decay must equal the total energy at the end of the decay. You must also account for the conversion of mass to energy and energy to mass. 2 Conservation of momentum. 3 Conservation of electric charge: The total number of charged particles may change, but the total amount of charge will not. 4 Conservation of nucleon number.

12 The decay reactions often continue through numerous steps. Eventually, a stable daughter nucleus is produced. Example: Original parent nucleus is U and the final product is Pb: β decays are indicated by horizontal arrows to the right. Diagonal arrows indicate alpha decays.

13 Outline

14 Individual nuclei decay one at a time, at random times: It is not possible to predict when a particular nucleus will decay (feature of quantum mechanics). The probability is specified in terms of the half-life of a given nucleus, t 1/2.

15 Individual nuclei decay one at a time, at random times: It is not possible to predict when a particular nucleus will decay (feature of quantum mechanics). The probability is specified in terms of the half-life of a given nucleus, t 1/2. Assume an initial number of nuclei, N 0, are present in a sample (t = 0):

16 Individual nuclei decay one at a time, at random times: It is not possible to predict when a particular nucleus will decay (feature of quantum mechanics). The probability is specified in terms of the half-life of a given nucleus, t 1/2. Assume an initial number of nuclei, N 0, are present in a sample (t = 0): At time t = t 1/2, half of the nuclei will have decayed. At time t = 2 t 1/2, a quarter of the nuclei will have decayed....

17 Individual nuclei decay one at a time, at random times: It is not possible to predict when a particular nucleus will decay (feature of quantum mechanics). The probability is specified in terms of the half-life of a given nucleus, t 1/2. Assume an initial number of nuclei, N 0, are present in a sample (t = 0): Decay constant, λ, is defined so that: N = N 0 e λ t t 1/2 = ln 2/λ

18 Individual nuclei decay one at a time, at random times: It is not possible to predict when a particular nucleus will decay (feature of quantum mechanics). The probability is specified in terms of the half-life of a given nucleus, t 1/2. Assume an initial number of nuclei, N 0, are present in a sample (t = 0): Decay constant, λ, is defined so that: N = N 0 e λ t t 1/2 = ln 2/λ

19 Activity The strength of a radioactive sample is measured using a property called its activity: The activity is proportional to the number of nuclei that decay in one second. The official SI unit of activity is the Becquerel (Bq): 1 Bq = 1 decay / s

20 Activity The strength of a radioactive sample is measured using a property called its activity: The activity is proportional to the number of nuclei that decay in one second. Another common unit is the Curie (Ci): 1 Ci = decays / s

21 Law of Activity A: A = dn / dt = λ N with solution: N(t) = N 0 e λ t and A = λ N 0 e λ t Mean lifetime τ: x ( x f (x) dx ) ( / ) f (x) dx τ = t dn(t) dn(t) = t e λ t dt 0 0 e λ t dt = 1 λ

22 Law of More common in nuclear physics (as introduced earlier): t 1/2 = ln 2 / λ = τ ln 2 half life For a decay chain: A B C... dn B (t) / dt = λ B N B + λ A N A N B (t) = ( λ A N A (0) e λ A t λ B λ A ) e λ B t

23 Outline

24 Odd-A Nuclei Mass Parabola even-odd / odd-even Example for A = 135 showing one stable nuclide with Z = 56. M(Z, A) = α A β Z + γ Z 2 + XXwith minimum at: Z = β / 2γ δ A 1/2

25 Even-A Nuclei Mass Parabola even-even / odd-odd Example for A = 104 Double β-decay (2nd-order weak interaction) First observed in 1987 ( 82 34Se Kr + 2e + 2 ν e ) Double electron capture never observed.

26 Even-A Nuclei Mass Parabola even-even / odd-odd Double β-decay (2nd-order weak interaction) First observed in 1987 ( 82 34Se Kr + 2e + 2 ν e ) Double electron capture never observed.

27 Outline

28 The biological effects of radioactivity result from the way the decay or reaction products interact with atoms and molecules: The typical binding energy of an electron in an atom is on the order of 10 ev. The energy released in a nuclear reaction is typically several MeV. If one of the particles collides with an atomic electron, there is enough energy to eject the electron from the atom or break a chemical bond in molecules.

29 The biological effects of radioactivity result from the way the decay or reaction products interact with atoms and molecules: The typical binding energy of an electron in an atom is on the order of 10 ev. The energy released in a nuclear reaction is typically several MeV. If one of the particles collides with an atomic electron, there is enough energy to eject the electron from the atom or break a chemical bond in molecules. The amount of damage that a particular particle is capable of doing is difficult to predict. α, β and γ radiation all have different masses and charges and therefore interact with tissue in different ways. The amount of kinetic energy carried by a particle also varies.

30 Measuring Damage 1 Radiation Absorbed Dose rad 1 rad is the amount of radiation that deposits 10 2 J of energy into 1 kg of absorbing material. The unit accounts for both the amount of energy carried by the particle and the efficiency with which the energy is absorbed (SI unit is Gray: 1 Gray = 1 Gy = 1 J / kg = 100 rad). 2 Relative Effectiveness RBE This measures how efficiently a particular type of particle damages tissue. This accounts for the fact that different types of particles can do different amounts of damage even if they deposit the same amount of energy.

31 Measuring Damage RBE value tends to increase as particle mass increases. Röntgen Equivalent in Man rem: Dose in rem = (dose in rad) RBE (RBE = 1 for 200 kev X rays) This combines the amount and also the effectiveness of the radiation absorbed. SI unit is Sievert (Sv): 1 rem = 0.01 Sv = 10 msv

32 Measuring Damage When the radiation dose is low, cells are sometimes able to repair the damage: Especially if dose is absorbed over long periods of time. Generally, small amounts of radiation do not cause significant harm to living cells. If the radiation dose is very large, then cells can be completely destroyed. At intermediate doses, cells survive but often malfunction as a result of the damage: A typical result is that the affected cells reproduce in an uncontrolled fashion, leading to cancer.

33 Radiation Damage Radiation damage is usually most severe for quickly dividing cells: Many types of blood and bone marrow cells fall into the category. Cancerous cells are also quickly dividing, so radiation can be used as a tool to selectively destroy cancer cells. Cancerous cells are also quickly dividing, so radiation can be used as a tool to selectively destroy cancer cells: For example, an alpha particle outside the body will be stopped in the outer layer of skin and do relatively little damage. If a person ingests an alpha particle it can do a great deal of damage to nearby cells.

34 Radiation Exposure Values

35 Radiation Exposure Values For common medical procedures, benefits usually outweigh the risk of exposure.

36 Radiation Exposure Values For common medical procedures, benefits usually outweigh the risk of exposure. Natural exposure occurs from many sources: Cosmic rays a collection of many different types of particles from outer space. Radon produced by the decay of U in rocks and soil.

37 Radiation Exposure Values For common medical procedures, benefits usually outweigh the risk of exposure. Natural exposure occurs from many sources: Cosmic rays a collection of many different types of particles from outer space. Radon produced by the decay of U in rocks and soil. Cancer Treatment: Radioactive materials emit high energy electrons or gamma rays that kill nearby cancer cells. Also, accelerators can be used (particle therapy).

38 Outline

39 Cosmic rays interacting with atmospheric nitrogen produce 14 6 C 14 6 C is radioactive with a T 1/2 = 5730 years. Carbon dating is done by measuring the ratio of 14 6 C / 12 6 C and observing the decrease due to the decay of the 14 6 C.

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