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Nuclear Reactions and Their Applications. Nuclear Reactions and Their Applications. Radioactive Decay and Nuclear Stability. The Kinetics of Radioactive Decay. Nuclear Transmutation: Induced Changes in Nuclei. Effects of Nuclear Radiation on Matter. Applications of Radioisotopes.
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Nuclear Reactions and Their Applications Radioactive Decay and Nuclear Stability The Kinetics of Radioactive Decay Nuclear Transmutation: Induced Changes in Nuclei Effects of Nuclear Radiation on Matter Applications of Radioisotopes Interconversion of Mass and Energy Applications of Fission and Fusion
Components of the Nucleus >99.9% mass of the atom lies in the dense, tiny nucleus. A nuclide is a nucleus with a particular composition. Each isotope of an element has a different nuclide. A particular nuclide is often designated by its mass number; for example, Cl-35 and Cl-37.
Notation for Nuclides The relative mass and charge of a particle is described by the notation: A = mass number Z = charge of the particle Example: 0 -1 1 1 1 0 e n p electron A X proton Z neutron
Nuclear Decay causes Radioactivity Many nuclides are unstable and spontaneously emit radiation, a process termed radioactive decay. - The intensity of the radiation is not affected by temperature, pressure, or other physical and chemical conditions. Nucear decay produces radiation and formation of new element(s). Three types of natural radioactive emission: Alpha particles (α, , or ) are identical to helium-4 nuclei. 4 2 4 2 0 -1 e α He2+ γ 0 0 Beta particles (β, β-, or ) are high-speed electrons. Gamma rays (γ or ) are very high-energy photons (hv).
Radioactive emissions in an electric field The positively charged α particles curve toward the negative plate, the negatively charged β particles curve towards the positive plate, and the γ rays are not affected by the electric field.
Nuclear Reaction and Nuclear Equation When a nuclide decays, it forms a daughter nuclide of lower energy. The excess energy is carried off by the emitted radiation and the recoiling nucleus of the daughter nuclide. The decay process is represented by a balanced nuclear equation. Both the total charge(#Z) and the total mass (#A) must be balanced: Total A Total Z Total A Total Z Reactants = Products
Modes of Radioactive Decay • Alpha (α) decay: Heavy nuclide decomposes into α particle and a lighter nuclide. • The product nuclide’s A decreases by 4 and Z decreases by 2. • Most common form of decay for a heavy, unstable nucleus. • β- decay produces β- particle and a new nuclide. • A remains the same in the daughter nuclide but Z increases by 1 unit. 228 88 63 28 Ra → Ni →
Positron (β+) emission produces β+ particle and a new nuclide. • The positron is the antiparticleof the electron. • A remains the same in the daughter nuclide but Z increases by 1 unit. • Electron capture: Parent nuclide combines an electron to form a new nuclide. • The effect on A and Z is the same as for positron emission. • Electron capture by Co-57: 11 6 C →
Gamma (γ) emission involves the radiation of high-energy γ photons. • Gamma emission usually occurs together with other forms of radioactive decay. • Several γ photons of different energies can be emitted from an excited nucleus as it returns to the ground state. • γ emission results in no change in either A or Z since γ rays have no mass or charge.
Practice Writing Equations for Nuclear Reactions Write balanced equations for the following nuclear reactions: (a) Thorium-232 undergoes α decay. (b) Zirconium-86 undergoes electron capture. (c) Potassium-40 undergoes beta emission (d) Magnesium-23 undergoes positron emission.
Nuclear Stability Two key factors determine the stability of a nuclide: - the number of neutrons (N), the number of protons (Z), and their ratio (N/Z), and - the total mass of the nuclide. A plot of number of neutrons vs. number of protons for all stable nuclides produces a band of stability that gradually curves above the line for N = Z. - Lighter nuclides are stable when N = Z. - As Z increases, the N/Z for stable nuclei gradually increases. - All nuclides with Z > 83 are unstable.
Stability and Nuclear Structure Protons within the nucleus experience electrostatic repulsive forces, which destabilize the nucleus. The strong force, which exists between all nucleons, counteracts the weaker repulsive forces. Nucleons are found in nucleon energy levels, and pairing of the spins of like nucleons leads to greater stability. - Elements with an even Z (number of protons) usually have a larger number of stable nuclides. - Over half the stable nuclides have both even N and even Z.
Stable Nuclides: Even or Odd matters! * Even Z shown in boldface.
The 238U decay series. A parent nuclide may undergo a series of decay steps before a stable daughter nuclide is formed.
Detection and Measurement of Radioactivity An ionization counter detects radioactive emissions as they ionize a gas. Ionization produces free electrons and gaseous cations Gaseous cations are attracted to electrodes and produce an electric current.
Detection and Measurement of Radioactivity Scintillation counter detects radioactive emissions by their ability to excite atoms and cause them to emit light. Radioactive particles strike a light-emitting substance, which emits photons. The photons strike a cathode and produce an electric current.
A scinatillation “cocktail” in tubes to be placed in the counter.
Units of Radioactivity The SI unit of radioactivity is the Becquerel (Bq), defined as one disintegration per second (d/s). The curie (Ci) is a more commonly used unit: 1 Ci = 3.70x1010 d/s
Units of Radiation The gray is the SI unit for energy absorption. 1 Gy = 1 J absorbed per kg of body tissue. The rad is more widely used: 1 rad = 0.01 J/kg or 0.01 Gy. The rem is the unit of radiation dosage equivalent to a given amount of tissue damage in a human. no. of rems = no. of rads x RBE The RBE is the relative biological effectiveness factor. The rem allows us to assess actual tissue damage by taking into account the strength of the radiation, the exposure time, and the type of tissue.
Rate of Radioactive Decay Radioactive nuclei decay at a characteristic rate, regardless of the chemical substance in which they occur. The rate (A) (= the activity) is the change in number of radioactive nuclide per unit of time Fact: The rate of radioactive decay is proportional to the number of nuclei present (N). A = kN k : decay constant. The largerk, the higher the activity of the substance.
How much radioactive nuclei remains/depleted depends on the Rate of Radioactive Decay Starting from N0 , at time t, the number of remaining nuclei Nt N0 Nt Nt N0 At A0 At time t, the radioactivity of remaining substance At = kNt= kN0e-kt ln = -kt or Nt = N0e-kt and ln = kt ln = -kt or At = A0e-kt
Half-Life of Radioactive Decay The half-life (t1/2) of a nuclide is the time taken for half the nuclei in a sample to decay (Nt = ½ N0 ) - The number of nuclei remaining is halved after each half-life. - The mass of the parent nuclide decreases while the mass of the daughter nuclide increases - Activity is halved with each succeeding half-life. When t = t1/2, Nt = ½ N0 , then
ln 2 k t1/2 = Half life of C-14: Loss of 14C nuclei over time
Decay Constants (k) and Half-Lives (t1/2) of Beryllium Isotopes 7 4 8 4 9 4 10 4 11 4
Example: Sr-90 occurs as nuclear test and, once ingested, poses long term health hazard. A woman drinks some contaminated milk and ingests 0.0500 g of 90Sr, which is taken up by bones and teeth and not eliminated. (a) How much 90Sr (t1/2 = 29 yr) is present in her body after 10 yr? k = 0.0239 yr-1, Nt= 0.039 g
Example: Sr-90 occurs as nuclear test and, once ingested, poses long term health hazard. A woman drinks some contaminated milk and ingests 0.0500 g of 90Sr, which is taken up by bones and teeth and not eliminated. (b) How long will it take for 99.9% of the 90Sr to decay? Nt = 5 x 10-5 g, t = 2.9 x 102 yr
Example: Given: Find: If a sample of 90Sr has an activity of 1.2x1012 d/s, what are the activity and the fraction of nuclei that have decayed after 59 yr (t1/2 of 90Sr = 29 yr)? N0 = 1.2x1012 d/s t1/2 = 29 yr t = 59 yr Equation: A = kN At At = e26.4 = 2.9x1011 d/s fraction decayed = 0.76
Radioisotopic Dating • Radioisotopes can be used to determine the ages of certain objects. • Radiocarbon dating measures the relative amounts of 14C and 12C in materials of biological origin. • 14C is formed from bombardment of 14N by neutrons • The ratio of 14C/12C remains the same for all living organisms. • Once the organism dies, the amount of 14C starts to decrease (forming 14N). • Since 14C decays at a predictable rate, measuring 14C/12C ratio indicates the time that has passed since the organism died. • 40K/40Ar ratios used to determine the age of certain rocks. A0 At ln 1 k t =
Ages of several objects determined by radiocarbon dating A0 At ln 1 k t =
PROBLEM: A sample of an ancient bone has a specific activity of 5.22 disintegrations per minute per gram of carbon (d/min·g). If 12C/14C ratio for living organisms results in a specific activity of 15.3 d/min·g, how old are the bones (t1/2 of 14C = 5730 yr)? Radiocarbon Dating A0 = 15.3 d/min g, At = 5.22 d/min g k = 1.21x10-4 yr-1 t = 8.89x103 yr
Nuclear Transmutation: Element X to Element Y Nuclear transmutation is the induced conversion of the nucleus of one element into the nucleus of another. How? High-energy bombardment of nuclei in a particle accelerator. 14 4 1 17 7 2 1 8 N + α → p + O
Formation of some Transuranium Nuclides* Reaction Half-life of Product 432 yr 163 days 4.5 h 45 min 239 94 239 94 242 96 241 95 253 99 253 99 18 8 4 2 4 2 4 2 4 2 1 0 242 96 245 98 241 95 256 101 243 97 256 101 1 0 0 -1 1 0 1 0 1 0 1 0 Pu + 2 n → Am + β Es + α → Md + n Pu + α → Cm + n Cm + α → Cf + n Am + α → Bk + 2 n Am + O → Lr + 5 n 76 min 28 s * Like chemical reactions, nuclear reactions may occur in several steps.
Schematic diagram of a linear accelerator The linear accelerator uses a series of tubes with alternating voltage. A particle is accelerated from one tube to the next by repulsion.
Effects of Nuclear Radiation on Matter Radioactive emissions collide with surrounding matter, knocking out electrons and causing ionization Each such event produces a cation and a free electron. The number of cation-electron pairs is directly related to the energy of the incoming ionizing radiation. Ionizing radiation has a destructive effect on living tissue. The danger of a particular radionuclide depends on - the type of radiation, - its half-life, and - its biological behavior.
Penetrating power of radioactive emissions The effect of radiation on living tissue depends on both the penetrating power and the ionizing ability of the radiation. Penetrating power is inversely related to the mass, charge, and energy of the emission.
Molecular Interactions with Radiation The interaction of ionizing radiation with molecules causes the loss of an electron from a bond or a lone pair. This results in the formation of free radicals, molecular or atomic species with one or more unpaired electrons. Free radicals are unstable and extremely reactive. Reaction between free radicals and live tissues will damage the tissue
Sources of Ionizing Radiation Natural sources of background radiation: • Cosmic radiation from the Sun and stars • Radon is a radioactive product of uranium and thorium decay. • Rn contributes to 15% of annual lung cancer deaths. • Radioactive 40K is present in water and various food sources. • Radioactive 14C occurs in atmospheric CO2.
Radioactive Tracers • The isotopes of an element exhibit very similar chemical and physical behavior. • A small amount of radioactive isotope mixed with the stable isotope will undergo the same chemical reactions, and can act as a tracer. • Radioactive tracers are used • to study reaction pathways, • to track physiological functions, • to trace material flow, • to identify the components of a substance from a very small sample, and • to diagnose a wide variety of medical conditions.
