Chapter 4: Nuclear Reactions PDF

Radiation Physics (46351) Radiation and Environment (42341) Chapter 4 NUCLEAR REACTIONS Prof. Dr. Khalil Thabayneh Hebron University - Palestine Nuclear reactions (1) Introduction In nuclear physics and nuclear chemistry, a nuclear reaction is considered to be the process...

Radiation Physics (46351) Radiation and Environment (42341) Chapter 4 NUCLEAR REACTIONS Prof. Dr. Khalil Thabayneh Hebron University - Palestine Nuclear reactions (1) Introduction In nuclear physics and nuclear chemistry, a nuclear reaction is considered to be the process in which two nuclei, or a nucleus and an external subatomic particle, collide to produce one or more new nuclides. Thus, a nuclear reaction must cause a transformation of at least one nuclide to another. If a nucleus interacts with another nucleus or particle and they then separate without changing the nature of any nuclide, the process is simply referred to as a type of nuclear scattering, but not a nuclear reaction. ، ‫إذا ﺗﻔﺎﻋﻠﺖ ﻧﻮاة ﻣﻊ ﻧﻮاة أو ﻣﻊ ﺟﺴﯿﻢ آﺧﺮ ﺛﻢ اﻧﻔﺼﻼ دون ﺗﻐﯿﯿﺮ ﻓﻲ طﺒﯿﻌﺔ أي ﻣﻦ اﻟﻨﻮاﺗﯿﻦ‬ ‫ وﻟﯿﺲ ﺗﻔﺎﻋﻞ ﻧﻮوي‬، ‫ﯾُﺸﺎر إﻟﻰ اﻟﻌﻤﻠﯿﺔ ﺑﺒﺴﺎطﺔ ﻋﻠﻰ أﻧﮭﺎ ﻧﻮع ﻣﻦ اﻟﺘﺸﺘﺖ اﻟﻨﻮوي‬.  Natural nuclear reactions occur in the interaction between cosmic rays and matter, and nuclear reactions can be employed artificially to obtain nuclear energy. Perhaps the most notable nuclear reactions are the nuclear chain reactions in fissionable materials that produce induced nuclear fission, and the various nuclear fusion reactions of light elements that power the energy production of the sun and stars. (2) Q-value and energy balance In writing down the reaction equation, in a way like to a chemical equation, one may in addition give the reaction energy on the right side: Target nucleus + projectile → Final nucleus + ejectile‫ ﻣﻘﺬوف‬+ Q Ex. , Q = 22.2 MeV  The reaction energy (the "Q-value") is: - Positive for exothermal reactions ‫طﺎردة ﻟﻠﺤﺮارة‬ - Negative for endothermal reactions‫ ﻣﺎص ﻟﻠﺤﺮارة‬, opposite to the similar expression in chemistry. On the one hand, it is the difference between the sums of kinetic energies on the final side and on the initial side. But on the other hand, it is also the difference between the nuclear rest masses on the initial side and on the final side (in this way, we have calculated the Q-value above). (3) Balancing Nuclear Reactions A balanced chemical reaction equation reflects the fact that during a chemical reaction, bonds break and form, and atoms are rearranged‫ ﯾﺘﻢ إﻋﺎدة ﺗﺮﺗﯿﺐ اﻟﺬرات‬, but the total numbers of atoms of each element are conserved and do not change. A balanced nuclear reaction equation indicates that there is a rearrangement during a nuclear reaction, but of subatomic particles rather than atoms‫ﻟﻠﺠﺴﯿﻤﺎت دون اﻟﺬرﯾﺔ ﺑﺪﻻ ﻣﻦ اﻟﺬرات‬. Nuclear reactions also follow conservation laws, and they are balanced in two ways: 1- The sum of the mass numbers of the reactants equals the sum of the mass numbers of the products. 2- The sum of the charges of the reactants equals the sum of the charges of the products. Example 1: The reaction of an α particle with magnesium-25 (2512Mg) produces a proton and a nuclide of another element. Identify the new nuclide produced. Example 2: The nuclide (12553I) combines with an electron and produces a new nucleus and no other massive particles. What is the equation for this reaction? Example 3: Write a balanced equation for each of the following nuclear reactions: (a) the production of 17O from 14N by α particle bombardment (b) the production of 14C from 14N by neutron bombardment (c) the production of 233Th from 232Th by neutron bombardment (d) the production of 239U from 238U by 21H bombardment  Example 4: Complete each of the following equations by adding the missing species: (a) 2713Al + 42He ⟶ ?? + 10n (b) 9923Pu + ?? ⟶ 9624Cm + 10n (c) 23592U ⟶ ?? + 13555Cs + 4 10n Example 5: Complete each of the following equations: (a) 73Li + ?? ⟶ 242He (b) 146C ⟶ 147N + ?? (c) 2713Al +42He ⟶?? + 10n (4) Types of nuclear reactions Nuclear reactions vary with the difference of projectile. Either it is a neutron, proton, deuteron, or alpha particle. First: Nuclear Interactions with Neutrons: There are different reaction products for a nuclear reaction with neutrons, and this difference is caused by a difference in the neutron energy with which the reaction began. Neutron – Gamma reaction (n,γ) This reaction occurs when the speed of neutrons is low, as the following: 27 Al13 + 10n [2813Al + γ] In this reaction, the result is the isotope of the interacting element ‫وﻓﻲ ھذا اﻟﺗﻔﺎﻋل ﯾﻛون اﻟﻧﺎﺗﺞ ﻧظﯾر ﻟﻠﻌﻧﺻر اﻟﻣﺗﻔﺎﻋل‬.  Neutron – Proton reaction (n, p) In this reaction, the proton binds ‫ﯾﺘﺤﺪ‬to the electron from the medium surrounding the nucleus and the proton converts into a hydrogen atom like the following reaction: 14 1 15 14 1 7 N + 0 n [ 7 N] 6 C + 1 H Neutron – Alpha reaction (n, α) In this reaction the neutron speed must be high. Such as: 27 1 27 + 24 4 13 Al + 0 n [ 13 Al] 11 Na + 2 He Neutron – Neutron reaction (n, n) This reaction takes place when the energy of the neutron is between (100 KeV – few MeV). In this reaction, the energy of the outside neutron is less than the energy of the entering neutron (projectile). The nucleus is left in an excited state, after which it reaches the state of stability by emitting gamma rays, and the resulting nucleus is the interacting nucleus. ‫ وﺑﻌﺪ ذﻟﻚ ﺗﺼﻞ إﻟﻰ‬، ‫ﺗﺘﺮك اﻟﻨﻮاة ﺑﺤﺎﻟﺔ ﻣﻦ اﻹﺛﺎرة‬ ‫ واﻟﻨﻮاة اﻟﻨﺎﺗﺠﺔ ھﻲ اﻟﻨﻮاة اﻟﻤﺘﻔﺎﻋﻠﺔ‬، ‫ﺣﺎﻟﺔ اﻻﺳﺘﻘﺮار ﺑﺈﺻﺪار أﺷﻌﺔ ﺟﺎﻣﺎ‬.  Neutron – 2 Neutron reaction (n, 2n) This reaction needs a high energy neutron to overcome ‫ﻟﻠﺘﻐﻠﺐ‬ the binding energy of a neutron. The result of this reaction is a isotope of the reacting nucleus with atomic weight less by one than the atomic weight of the reactant material , such as the following reaction: 27 1 26 1 13 Al + 0 n (fast) 13 Al + 2 0 n The neutron reaction that leads to nuclear fission It is a reaction between fast or slow neutrons with heavy nuclei Z > 92. This interaction produces a number of neutrons, two intermediate nuclei, and a high energy of 200 Mev per fission, and will be identified later‫ ﺳﯿﺘﻢ ﺗﺤﺪﯾﺪه ﻻﺣﻘﺎ‬. Second: The Nuclear Reactions with Protons Nuclear reactions with protons differ according to the kinetic energy of the projectile (proton), and the proton is the nucleus of the hydrogen atom. Some proton reactions include: Proton – Alpha reaction (p, α) This reaction results a different nucleus and a helium nucleus, such as: 27 1 13 Al + 1 H [ 2814Si]* 24 12 Mg + 4 2 He 19 9 F + 1 1H [ 2010Ne]* 16 8 O + 4 2 He Proton – Neutron reaction (p, n) This reaction is always endothermic ‫ ﻣﺎص ﻟﻠﺤﺮارة‬,this is due to the fact that the sum of the resulting materials weights is greater than the sum of the reactions weights, because the weight of the neutron is greater than the weight of the proton, for example: 18 1 8 O + 1 H [199F] 18 9 F + 1 0 n  Proton – Gamma reaction (p, γ) In this reaction, high-energy gamma rays are produced as one of the reaction products, such as: 27 1 10 * 28 13 Al + 1 H [ 5 B] 14 Si + γ Proton - Deuteron reaction (p, d) In this reaction, the result is a isotope of the interacting nucleus, such as: 9 1 10 * 8 2 4 Be + 1 H [ 5 Be] 4 Be + 1 H A deuteron is a heavy hydrogen that contains a proton and a neutron. Third: The Nuclear Reactions with Deuterons There are three types of nuclear reactions with deuterons, and the deuteron is produced by the cyclotron with a high energy up to several MeV. Among these interactions are the following: Deuteron - Alpha reaction (d, α) This reaction is exothermic and the examples of this reaction include: 27 2 29 * 25 4 13 Al + 1 H [ 14 Si] 12 Mg + 2 He 16 2 18 * 14 4 8 O + 1 H [ 8 F] 7 N + 2 He Deuteron - Proton reaction (d, p) This type of reaction is exothermic and the resulting nucleus is a isotope of the interacting nucleus, such as: 23 2 25 * 24 1 11 Na + 1 H [ 12 Mg] 11 Na + 1 H 31 2 33 * 32 1 15 P + 1 H [ 16 S] 15 P + 1 H  Deuteron - Neutron reaction (d, n) The examples of this reaction include: 12 2 14 * 13 1 6 C + 1 H [ 7 N] 7 N + 0 n 9 2 11 * 10 1 4 Be + 1 H [ 9 B] 5 B + 0 n Fourth: The Nuclear Reactions with Alpha There are only two types of alpha reaction in which the result is either a neutron or proton: Alpha - Neutron reaction (α, n) The examples of this reaction include: 27 4 31 * 30 1 13 Al + 2 He [ 15 P] 15 P + 0 n 23 4 27 * 26 1 11 Na + 2 He [ 13 Al] 13 Al + 0 n  Alpha - Proton reaction (α, p) The examples of this reaction include: 17 4 31 * 30 1 13 Al + 2 He [ 15 P] 14 Si + 1 H Fifth: Gamma-Ray Interactions From the nuclear gamma-ray reactions is: Gamma - Neutron reaction (γ, n) The examples of this reaction include: 9 9 * 8 1 4 Be + γ [ 4 Be] 4 Be + 0 n 31 31 * 30 1 15 P + γ [ 15 P] 15 P + 0 n When the energy of gamma rays is high, a gamma-proton reaction can occur (γ, p) Sixth: Nuclear Fission Nuclear fission is a process in nuclear physics or nuclear chemistry in which the heavy nucleus of an atom (A > 200) splits into two or more smaller nuclei as fission products, and usually some by-product particles ‫ ﺑﻌﺾ اﻟﻤﻨﺘﺠﺎت اﻟﺜﺎﻧﻮﯾﺔ‬. The by-products ‫اﻟﻤﻨﺘﺠﺎت اﻟﺜﺎﻧﻮﯾﺔ‬include free neutrons, photons usually in the form gamma rays, and other nuclear fragments such as beta particles and alpha particles. Fission of heavy elements is an exothermic reaction and can release substantial amounts of useful energy both as gamma rays and as kinetic energy of the fragments (heating the material where fission takes place). Nuclear fission produces energy for nuclear power and to drive explosion of nuclear weapons.  In nuclear fission, an unstable atom splits into two or more smaller pieces that are more stable, and releases energy in the process. The fission process also releases extra neutrons, which can then split additional atoms, resulting in a chain reaction that releases a lot of energy. The energy released by nuclear fission is very huge. For example, the fission of one kilogram of uranium releases as much energy as burning around four billion kilograms of coal. In the process of nuclear fission, atoms are split to release that energy. A nuclear reactor, or power plant, is a series of machines that can control nuclear fission to produce electricity. The fuel that nuclear reactors use to produce nuclear fission is pellets ‫ ﻛﺒﺴﻮﻻت‬of the element uranium. Total BE would increase which means that the daughters are more stable than parent. Spontaneous fission is very rare. Uranium is the largest nucleus found on Earth. Its isotopes will sometimes fission naturally. But half-life for U-235 is 7×108 years Typical fission events release about 200 MeV of energy, the equivalent of roughly > 2 trillion Kelvin, for each fission event compared to burning coal which only gives a few eV. The minimum mass capable of supporting sustained fission is called the critical mass. This amount depends on the purity of the material and the shape of the mass, which corresponds to the amount of surface area available from which neutrons can escape, and on the identity‫ﻧﻮع‬ of the isotope.  Types of Fission (a) Induced Fission ♥ Fission of 235U by a slow (low energy) neutron – 236U* is an intermediate, short-lived state Lasts about 10-12 s – X and Y are called fission fragments ♠ Many combinations of X and Y satisfy ‫ ﺗﻔﻲ‬the requirements of conservation of energy and charge. ♥ Examples: 23 U 1n 13 Cs 96 R 1 592 + 0 855 + 37 + n 20  The fission products have a ratio of N/Z much too high to be stable for their A value. The sum of the masses of these fragments is less than the original mass. This 'missing' mass (about 0.1 percent of the original mass) has been converted into energy according to Einstein's equation (E = mc2). (b) Thermal Neutron Fission Fission fragments are highly unstable because they are so neutron rich. Fasting neutrons are emitted simultaneously with the fissioning process. Even after fasting neutrons are released, the fission fragments undergo beta decay, releasing more energy. Most of the ~200 MeV released in fission goes to the kinetic energy of the fission products, but the neutrons, beta particles, neutrinos, and gamma rays typically carry away 30–40 MeV of the kinetic energy. (c) Chain Reaction ♥ Neutrons are emitted when 235U undergoes fission ♥ These neutrons are then available to trigger fission in other nuclei ♥ This process is called a chain reaction – If uncontrolled, a violent ‫ ﻋﻨﯿﻒ‬explosion can occur – The principle behind the nuclear bomb, where 1 kg of U can release energy equal to about 20 000 tons of TNT ► Fission Reactors Several components are important for a controlled nuclear reactor: 1) Fissionable fuel ‫وﻗﻮد ﻗﺎﺑﻞ ﻟﻼﻧﺸﻄﺎر‬ 2) Moderator to slow down neutrons‫ﻣﮭﺪئ ﻹﺑﻄﺎء اﻟﻨﯿﻮﺗﺮوﻧﺎت‬ 3) Control rods for safety and to control criticality ‫ اﻟﺤﺎﻟﺔ اﻟﺤﺮﺟﺔ‬of reactor 4) Reactor vessel and radiation shield 5) Energy transfer systems if commercial power is desired‫ﻣﻄﻠﻮب‬ Two main effects can “poison” reactors: ‫ﯾﻤﻜﻦ أن ﯾﺆدي ﺗﺄﺛﯿﺮان رﺋﯿﺴﯿﺎن إﻟﻰ‬ :‫"ﺗﺴﻤﯿﻢ" اﻟﻤﻔﺎﻋﻼت‬ (1) neutrons may be absorbed without producing fission. ‫ﯾﻤﻜﻦ اﻣﺘﺼﺎص اﻟﻨﯿﻮﺗﺮوﻧﺎت دون إﻧﺘﺎج اﻧﺸﻄﺎر‬ (2) neutrons may escape from the fuel zone. ►Types of Reactors Power reactors produce commercial electricity. Research reactors are operated to produce high neutron fluxes for neutron-scattering experiments. Heat production reactors supply heat in some cold countries. Some reactors are designed to produce radioisotopes. Several training reactors are located on college campuses. Some reactors are designed to produce nuclear weapons. Some reactors are designed to used to desalinate sea water ► Nuclear Reactor Problems 1- The danger of a serious accident in which radioactive elements are released into the atmosphere or groundwater is of great concern to the general public. 2- Thermal pollution both in the atmosphere and in lakes and rivers used for cooling may be a significant ecological ‫ ﺑﯿﺌﯿﺔ‬problem. 3- A more serious problem is the safe disposal of the radioactive wastes produced in the fissioning process, because some fission fragments have a half-life of thousands of years. 4- Many widely publicized accidents at nuclear reactor (it was mentioned earlier) ‫اﻟﻌﺪﯾﺪ ﻣﻦ ﺣﻮادث اﻟﻤﻔﺎﻋﻞ اﻟﻨﻮوي اﻟﺘﻲ ﺗﻢ اﻹﻋﻼن ﻋﻨﮭﺎ ﻋﻠﻰ ﻧﻄﺎق واﺳﻊ )ﺗﻢ‬ (‫ذﻛﺮھﺎ ﺳﺎﺑﻘًﺎ‬ 5- Large expansion of nuclear power can succeed only if four critical problems are overcome: lower costs, improved safety, better nuclear waste management, and lower proliferation risk. ‫ اﻧﺨﻔﺎض اﻟﺘﻜﺎﻟﯿﻒ‬:‫ ﻻ ﯾﻤﻜﻦ أن ﯾﻨﺠﺢ اﻟﺘﻮﺳﻊ اﻟﻜﺒﯿﺮ ﻓﻲ اﻟﻄﺎﻗﺔ اﻟﻨﻮوﯾﺔ إﻻ إذا ﺗﻢ اﻟﺘﻐﻠﺐ ﻋﻠﻰ أرﺑﻊ ﻣﺸﺎﻛﻞ ﺣﺮﺟﺔ‬.‫ وﺗﻘﻠﯿﻞ ﻣﺨﺎطﺮ اﻻﻧﺘﺸﺎر‬، ‫ وإدارة أﻓﻀﻞ ﻟﻠﻨﻔﺎﯾﺎت اﻟﻨﻮوﯾﺔ‬، ‫ وﺗﺤﺴﯿﻦ اﻟﺴﻼﻣﺔ‬، Seventh: Nuclear Fusion Nuclear fusion is the process of making a single heavy nucleus (part of an atom) from two lighter nuclei. This process is called a nuclear reaction. It releases a large amount of energy. The nucleus made by fusion is heavier than either of the starting nuclei.... Hydrogen atoms are fused together to make helium. Fusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion reactions.... Fusion processes require fuel and a confined environment with sufficient temperature, pressure, and confinement time to create a plasma in which fusion can occur. The following advantages make fusion worth pursuing. Abundant energy: Fusing atoms together in a controlled way releases nearly four million times more energy than a chemical reaction such as the burning of coal, oil or gas and four times as much as nuclear fission reactions (at equal mass).  The Sun is a main-sequence star, and, as such, generates its energy by nuclear fusion of hydrogen nuclei into helium. In its core, the Sun fuses 620 million tons of hydrogen and makes 606 million tons of helium each second. Energy released in fusion reactions. Energy is released in a nuclear reaction if the total mass of the resultant particles is less than the mass of the initial reactants.... The particles a and b are often nucleons, either protons or neutrons, but in general can be any nuclei. Every second, our Sun turns 600 million tonnes of hydrogen into helium, releasing an enormous amount of energy. But without the benefit of gravitational forces at work in our Universe, achieving fusion on Earth has required a different approach. We find that the temperature inside the sun reaches 108 Kelvin. ▪ When two small nuclei the product of fusion would have more BE per nucleon. ▪ The increases in binding energy per nucleon are much larger for fusion than for fission reactions, because the graph increases more steeply for light nuclei. ▪ So fusion gives out more energy per nucleon involved in the reaction than fission.  A high-temperature reaction is called a thermo nuclear reaction. The most common thermonuclear reactions in stars are the proton-proton cycle and the carbon cycle. ► Proton- Proton Cycle 1 1 H + 11H 2 1 H + β - + γ + 0.42 Mev 2 1 H + 11H 3 2 H + γ + 5.49 Mev 3 2 H + 32H 4 2 He + 2 1 1 H + 12.86 Mev ► Carbon Cycle 126C + 11H 13 7 N + γ + 1.95 Mev 137N + 11H 13 6 C + β + + γ + 1.26 Mev 136C + 11H 14 7 N + γ + 7.55 Mev 147N + 11H 15 8 O + γ + 7.34 Mev 158O + 11H 15 7 N + β - + γ + 1.68 Mev 157N + 11H 12 6 C + 4 2 He + 4.96 Mev The total energy of the reaction is 24.68 Mev.  Nuclear thermal reactions have been studied in the laboratory including hydrogen isotopes (deuterium 2H and tritium 3H). 2 3 4 1 H + 1 H 2 He + n + 17.6 Mev 2 2 3 1 H + 1 H 2 He + n + 3.2 Mev 2 2 3 1 1 H + 1 H 1 H + 1 H + 4.0 Mev 2 H + 3H → 4He + 1n + → +  Energy Released To calculate the energy released during mass destruction in both nuclear fission and fusion, we use Einstein’s equation that equates energy and mass: E = mc2 Where m is mass (in kilograms), c is speed of light (in m/s) and E is energy (in Joules). For the reaction: A + B C+D The total energy must be conserved. ∆Q =[(mA + mB) - (mC +mD)] c2 Example (7): Calculate the amount of energy (in electron volts per atom and kilo joules per mole) released when the neutron-induced fission of 235U produces 144Cs, 90Rb, and two neutrons: Example (8): In the thermal neutron capture Calculate the amount of energy in MeV? Example (9): In the nuclear reaction Calculate the amount of energy in MeV? Ex. (10): Calculate the amount of energy (in electron volts per atom and kilo joules per mole) released when deuterium and tritium fuse to give Helium-4 and a neutron: Answer: ΔE = −17.6 MeV/atom = −1.697 × 109 kJ/mol