Nuclear Chemistry PDF

Nuclear Chemistry Nuclear chemistry has many applications in knowing facts from the past, present, and future. From half-life of elements up to extraterrestrial bodies, nuclear chemistry plays an important role. In this topic, the students will understand the equations and reactions involved in nuc...

Nuclear Chemistry Nuclear chemistry has many applications in knowing facts from the past, present, and future. From half-life of elements up to extraterrestrial bodies, nuclear chemistry plays an important role. In this topic, the students will understand the equations and reactions involved in nuclear chemistry. Some of the vital and diversified applications of nuclear chemistry are discussed further with factual problems for student’s exercise. The Spitzer Space Telescope, which is sensitive to infrared radiation, is shown here against an infrared image of the sky. Because the intensity of cosmic rays increases with altitude, electronic equipment on satellites such as Spitzer is especially susceptible to damage from ionizing radiation. Courtesy of NASA, JPL/Caltech Outcomes At the end of discussion, the student should be able to:  Understand radioactivity  Describe cosmic rays and how they influence Earth and atmosphere.  Write, balance, and interpret equations for simple nuclear reactions.  Define modes of nuclear decay which includes alpha decay, beta decay, positron emission, and electron capture.   Interpret the kinetics of radioactive decay using first-order rate equations.  Use Einstein’s equation.  Describe nuclear fission and fusion.  Discuss the potential of both fission and fusion as energy sources.  Explain penetrating power and ionizing power.  Solve applications of radioisotopes. Introduction Nuclear Chemistry is the branch of chemistry that deals with the changes in the nuclei. Conventional energy sources, such as coal, petroleum will be exhausted in the near future. Scientists are searching non-conventional energy sources such as solar-energy, nuclear energy etc. Utilization of nuclear energy came after the discovery of radioactivity. For solar energy, we have cosmic rays. Cosmic Rays are subatomic particles traveling at high speeds that constantly bombard Earth. Majority are atomic nuclei: 87% hydrogen nuclei, 12% helium nuclei, and the rest are heavier nuclei. It can originate outside the solar system. Cosmic rays originate from solar flares on the sun, which can accelerate highly charged cations until they approach the speed of light. The distribution of atomic nuclei reflects composition of the sun. Hydrogen and helium are the most prevalent. Carbon, nitrogen, oxygen, neon, magnesium, silicon, and iron are also present. The energies of cosmic rays are much higher than in other areas of chemistry. Chemical energies usually measured in kJ/mol. Also, cosmic ray energies can be measured in electron volts (eV), where 1 eV = 96.5853 kJ mol-1 (cosmic rays are in the MeV or GeV range). Upon entering the atmosphere, cosmic rays start to collide with gas molecules and induce nuclear reactions; for an instance, the formation of radioactive 14C. When a free neutron is absorbed by a nitrogen nucleus, a proton is emitted and 14C is produced. The terrestrial carbon is 98.9% 12C and 1.11% 13C. Both are stable, however, 14C is unstable and undergoes spontaneous radioactive decay. Particles are ejected and a nitrogen atom is formed. Radioactivity Becquerel in 1896 observed that uranium or its compounds emit a kind of rays spontaneously. These rays can affect photographic plate. He named this phenomenon of emission of spontaneous radiation by uranium as radioactivity. The atoms of some of the elements were found to exhibit radioactivity, such as radium, thorium, polonium etc. As compounds of those elements exhibit radioactivity, so it can be said that radioactivity is a nuclear phenomenon. Radioactive elements emit the radiation and create new elements. Radioactivity is an irreversible process and emits more heat than that of any of the chemical processes (109 cal mol-1). After discovery of Uranium’s radioactivity, Ernest Rutherford demonstrated two distinct types of radiation. One type was stopped by thin pieces of aluminum, alpha rays. The second type passed through the aluminum, beta rays. In magnetic field, alpha and beta rays are deflected which indicates carrying a charge. Alpha and beta rays were deflected in opposite directions, indicating they held opposite charges. One type of particle was deflected more than the other indicating their mass to charge ratios were different. A third type of radiation, gamma rays, was revealed and which passed through the magnetic field undeflected. Figure 1: A thin sheet of aluminum blocks alpha rays but not beta rays. In a magnetic field, beta and alpha particles are deflected in different directions, while gamma rays are undeflected. Alpha particles, α, are the more massive and positively charged particles. Alpha particles are helium nuclei, 42𝐻𝑒. Beta particles, 𝛽 − 𝑜𝑟 −10𝛽 , are lighter and negatively charged. Beta particles are electrons, −10𝑒 , emitted from the nucleus. Gamma rays, γ, are the particles unaffected by the magnetic field. Gamma rays are high-energy photons of electromagnetic radiation emitted by the nucleus, 00𝛾.  Table 1. Comparison among α, β, and γ rays Radioactive Decay Nuclear reactions are written in a format similar to chemical reactions. Reactants and products are atoms or subatomic particles instead of molecules. Nuclide symbols (E) are written to represent the composition of a nuclide. 𝑚𝑎𝑠𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 𝑎𝑡𝑜𝑚𝑖𝑐 𝑛𝑢𝑚𝑏𝑒𝑟 𝐸 These symbols can be used to represent atoms, ions, and nuclei. Nuclide symbols for subatomic particles are the following: 𝑁𝑒𝑢𝑡𝑟𝑜𝑛, 10𝑛 𝑃𝑟𝑜𝑡𝑜𝑛, 11𝑝 𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛, −10𝑒 Atomic number is equivalent to the charge of the nucleus. Nuclear reactions are written using nuclide symbols. 14 7𝑁 + 10𝑛 → 14 6𝑁 + 11𝑝 Nuclear reactions are balanced when the sums of the mass numbers and atomic numbers for both sides of the equation are equal. For the radioactive decay, it follows an exponential law. At any instant of time, the rate of disintegration is proportional to the number of atoms (N) present, i.e., 𝑑𝑁 𝑑𝑁 𝑑𝑁⁄𝑑𝑡 − ∝ 𝑁 𝑜𝑟 − = 𝜆𝑁 𝑜𝑟 𝜆 = 𝑁dt 𝑑𝑡 𝑁 Where λ = disintegrating constant, may be defined as the ratio of the amount of the substance which disintegrates in a unit time`to the amount of the substance present. The negative sign indicates that with passage of time ‘t’ the number of atoms decreases. 𝑑𝑁 So, = −𝜆𝑑𝑡 𝑁 Integrating we have, 𝑙𝑜𝑔𝑒 𝑁 = −𝜆𝑡 + 𝐶 [C = integration constant] Let ‘𝑁0 ’ be the number of atoms present initially, i.e., when t=0 Then 𝑙𝑜𝑔𝑒 𝑁0 = 𝐶 Therefore, 𝑙𝑜𝑔𝑒 𝑁 = −𝜆𝑡 + 𝑙𝑜𝑔𝑒 𝑁0 𝑁 Or 𝑙𝑜𝑔𝑒 𝑁 = −𝜆𝑡 0 Thus, 𝑁 = 𝑁0 𝑒 −𝜆𝑡 When M0 = original mass and M = mass at a time t, the equation becomes 𝑀 = 𝑀0 𝑒 −𝜆𝑡 Hence, the decay curve is exponential in nature. Figure 2. Decay of Radioactive Substance If t is the half-life of the radioactive element, then we can write, 𝑁 1 = = 𝑒 −𝜆𝑡 𝑁0 2 𝑙𝑜𝑔𝑒2 0.693 Thus, 𝑡= =. 𝜆 𝜆 The above equation is a relation between half-life of a radioactive element and its disintegration constant. Half-life is the time required for half- of the atom to decay away. Half-lives for radioactive isotopes can be short as a fraction of a second or as long as millions of years, see Table 2. Table 2. Half-lives of some Radioactive Isotopes The unit of radioactivity is curie. The curie is defined as that quantity of any radioactive substance which gives 3.7 x 1010 disintegrations per second (Bq). The curie is a very large unit. Hence for all practical purposes millicurie [1 mCi = 10 -3] and the microcurie [1 µCi = 10 -6] are used. Problem 1 The half-life of carbon-14 used in radiocarbon dating, is 5730 years. What is the decay constant for carbon-14? Problem 2 Assuming that it was to remain undisturbed since 1898 A.D., calculate how much of Madam Curie’s 200 mg of radium would be left in the year 8378 A.D. (t 1/2 of radium is 1620 years). Problem 3 A radioactive source contains one microgram (µg) of 𝑃𝑢239. This source is estimated to emit 2300 α-particles / sec. in all directions. Estimate half-life of 𝑃𝑢239 from this data. Radiocarbon Dating 14 C is continually formed through the interaction of cosmic rays with the atmosphere. The 14C is incorporated into living plants and animals and the 14C/12C ratio remains constant over time. When a plant or animal dies, 14C is no longer incorporated and its activity decreases with time. An artifact’s age is determined by measuring its 14C/12C ratio and then comparing it to the 14C/12C ratio of living organisms. First order kinetics equations are used to determine the age of the artifact. Dendrochronology, which is based on counting growth rings in long-lived trees, has been used to calibrate carbon dating. Ages are determined to within ±40 to 100 years. Objects less than 60,000 years old can be carbon dated. Problem 4 A piece of cloth is discovered in a burial pit in the Philippines. A tiny sample of the cloth is burned from CO2, which is then analyzed. The 14C/12C ratio is 0.250 times the ratio in today’s atmosphere. How old is the cloth? Alpha Decay During alpha decay, an alpha particle is emitted from the nucleus. The mass number decreases by 4. The atomic number decreases by 2. 238 234 92𝑈 → 90𝑇ℎ + 42𝐻𝑒 The reactant nucleus is the parent and the product nucleus is the daughter. Problem 5 Complete the equations for each of the following nuclear decay processes.  210 206 84𝑃𝑜 → 82𝑃𝑏+ ? 230 90𝑇ℎ → ? + 42𝐻𝑒 Beta Decay During beta decay, a beta particle and an antineutrino, ṽ, are emitted from the nucleus. A neutron decays into a proton, a beta particle, and an antineutrino. The proton remains in the nucleus. A neutron decays into a proton, a beta particle, and an antineutrino. The proton remains in the nucleus. 1 0𝑛 → 11𝑝 + 0 −1𝛽 +ṽ The atomic number increases by 1. 14 14 0 6𝐶 → 7𝑁 + −1𝛽 +ṽ Problem 6 Complete the equations for each of the following nuclear decay processes. 234 234 90𝑇ℎ → 91𝑃𝑎+ ? 234 91𝑃𝑎 → ? + −10𝛽 + ṽ Binding Energy Binding energy is the energy released when a nucleus is formed from a collection of free nucleons. Binding energy is also the energy required to take apart a nucleus. The greater the binding energy, the more stable the nucleus. In 1905, Einstein established from theoretical standpoint that mass and energy are mutually convertible. The famous equation in this regard is 𝐸 = 𝑚𝑐 2 Where E = energy; c = velocity of light A Helium-4 atom is composed of 2 protons and 2 neutrons. Each proton has a mass of 1.00727647 atomic mass unit (amu). Each neutron has a mass of 1.0086649 amu. The sum of 2 protons and 2 neutrons is 4.03188278 amu. The difference between calculated mass and measured mass is the mass defect, ∆𝑚. The atomic mass of helium is 4.002602 amu. Thus, the ∆𝑚 for helium is 0.02928078 amu. The missing mass is converted to binding energy, according to Einstein equation:  1.661 × 10−27 𝑘𝑔 𝑚 2 𝐸 = (0.02928078 amu × ) (299792458 ) 1 𝑎𝑚𝑢 𝑠 𝐸 = 4.37113 × 10−12 𝐽 The energy released for one 42𝐻𝑒 nucleus is 4.37113 × 10−12 𝐽. For one mole of 42𝐻𝑒 , the energy released is 4.37113 × 10−12 𝐽 6.02214 × 1023 𝑎𝑡𝑜𝑚𝑠 𝐸=( )( ) 1 𝑎𝑡𝑜𝑚 42𝐻𝑒 𝑚𝑜𝑙 𝐸 = 2.63236 × 1012 𝐽⁄𝑚𝑜𝑙 Problem 7 Calculate the energy released by a nucleus of uranium-235 if it splits into a barium-141 nucleus and a krypton-92 nucleus according to the equation below. 235 92𝑈 + 10𝑛 → 236 92𝑈 → 141 56𝐵𝑎 + 92 36𝐾𝑟 + 3 10𝑛 Transmutation, Fission, and Fusion There are three categories of nuclear reactions: transmutation, where one nucleus changes into another, either by natural decay or in response to some outside intervention; fission, a heavy nucleus splits into lighter nuclei; fusion, light nuclei merge into a heavier nucleus. Transmutation 10 B reacts via neutron capture to produce 11B, an unstable intermediate nucleus called the compound nucleus, which decays almost instantly like an activated complex in a chemical reaction. The compound nucleus decays almost instantly, emitting particles and energy to produce a stable nucleus. 10 5𝐵 + 10𝑛 → 11 5𝐵 → 73𝐿𝑖 + 42𝐻𝑒 Nuclear Fission In 1939, German scientist Hahn and Strasman bombarded uranium atom with neutrons and obtained two elements with atomic numbers 56 and 36. 235 92𝑈 + 10𝑛 → 236 92𝑈 → 141 56𝐵𝑎 + 92 36𝐾𝑟 + 3 10𝑛 This phenomenon of splitting a nucleus into two approximately equal fragments is called nuclear fission or simply fission. The generated neutrons again can bombard another 235U atoms and another fission can occur and this phenomenon will occur within 10 -8 sec. This process of repeated fission is known as chain reaction and as a result it can generate a huge amount of energy, 1 g of U-235 will generate 2 x 107 kcal, and this amount of energy will be generated within 10 -6 second. The generation of huge amount of energy leads to an explosion wit a temperature of one crore degree. This nuclear fission reaction is the principle of atomic bomb. 235 Figure 3. Chain reaction as a result of bombardment of 92𝑈 with one neutron and three secondary neutrons are released. Energy released in a Fission Reaction It has been estimated that the mass generated after fission is not equal to the total weight of uranium underwent fission and bombarding neutrons. A small fraction of mass is lost and is converted to energy according to the equation: E = mc2 For the reaction, 235 92𝑈 + 10𝑛 → 236 92𝑈 → 141 56𝐵𝑎 + 92 36𝐾𝑟 + 3 10𝑛 The mass lost is 0.2153 amu which is equivalent to an energy of ≈ 200 𝑀𝑒𝑉 Highlight: It can be shown that when 1 kg of uranium had completely underwent fission, the energy released would be 8.2 x 1013 J, which is sufficient to supply energy at the rate of 2.2 megawatt continuously for one year. To utilize the energy released during the fission, we are to control the chain reaction to get heat energy according to necessity. Now a days, in an atomic reactor, the motion of neutrons are retarded by graphite or heavy water to control the chain reaction. Once retarded and controlled, the heat generated is being absorbed by molten Na-K alloy and this heat is utilized in generating steam for thermal power. Atomic Fusion At a very-high temperature, two nuclei combine to give comparatively heavy nucleus, i.e., two nuclei combine to give a new atom. This phenomenon is known as atomic fusion. And during this fusion reaction some mass is destroyed, that means such a fusion process would also lead to liberation of huge amount of energy which causes explosion. 2 1𝐻 + 21𝐻 → 42𝐻 𝑒 + 𝐸𝑛𝑒𝑟𝑔𝑦 This fusion released about 26.6545 MeV. The difficulty is to attain the high temperature for such fusion process. But it is believed that such condition is attained for preparing thermonuclear bomb such as hydrogen bomb. The transformations for fusion reactions are: 3 i. 1𝐻 + 21𝐻 → 42𝐻 𝑒 + 10𝑛 + 17 𝑀𝑒𝑉 3 ii. 1𝐻 + 11𝐻 → 42𝐻 𝑒 + 20 𝑀𝑒𝑉 Nuclear Reactors A nuclear reactor is an apparatus in which nuclear fission is produced in the form of a controlled self-sustaining chain reaction. It is a device where nuclear fission of U-235, U-233, Pu-239 and chain reaction takes place and produces heat, neutrons, and radio-isotopes. The uranium oxide fuel is embedded into fuel rods and placed in a water-covered reactor core. The water carries heat released to the steam turbine. Steam turns the turbine which generates electricity. The chain reaction is initiated by a source of neutrons. The chain reaction is regulated via control rods. The control rods are inserted between the fuel rods to slow or stop the chain reaction. Control rods are composed of cadmium or boron and regulate the chain reaction by absorbing extra neutrons to maintain a steady rate of fission. Figure 4. The general design used in all U.S. Nuclear Power Plants Nuclear Waste Several of the fission products in a nuclear reactor are radioactive. The radioactive products are concentrated in the used or “spent” fuel rods. The fuel rods are referred to as high-level nuclear waste. The half-lives of several of the products are very long, requiring special storage or disposal. Spent fuel rods can be reprocessed into new fuel rods. Reprocessing is not carried out in the United States due to regulatory concerns and nuclear nonproliferation treaties. All high-level waste is currently stored on-site at the reactor. On-site storage is not a long-term solution. Yucca Mountain, in southwest Nevada, was proposed as the site for an extensive feasibility study for long term storage of high-level waste because it fulfills several general engineering considerations. Yucca Mountain is extremely remote, the climate is dry, and the water level is about 1000 feet below the potential burial vault. The storage facility must remain intact for thousands of years. The construction materials will need to withstand the effects of high levels of radiation. Nuclear reactors are of various types depending on their neutron spectrum, construction, composition and purpose for which they are used. The reactors are differentiated by the following features.  Neutron energies: (a) High energy as in fast reactors (b) Intermediate energy (c) Low energy as in thermal reactors Interaction of Radiation and Matter There are three factors governing the effects of radiation on matter: The amount of radiation to which matter is exposed, Penetrating power of the radiation, and  Ionizing power of the radiation. If radiation energy is greater than typical ionization energies for atoms and molecules, the radiation could induce ionization in material encountered. Radiation is classified as either ionizing or nonionizing. The distinction is based on the energy carried by a photon or particle. Nonionizing radiation includes visible light, radio waves and microwaves where photon energies are less than typical ionization energies. Ionizing radiation includes alpha and beta particles, X-rays, and gamma rays where photon energies are greater than typical ionization energies. Ionization radiation can cause significant damage to any material encountered, including living tissue, by free radical formation. It rejects electrons from atoms and molecules it encounters. Meanwhile, free radicals scavenge electrons from other molecules, causing damage to tissue. Through free radical formation, ionizing radiation can lead directly to cell death. On the other hand, penetrating power must be taken into account when examining the impact of radiation on matter. In definition, penetrating power is how far a particle penetrates into a material before its energy is absorbed or dissipated. Alpha particles have greater ionizing power. The relatively large size and charge of alpha particles prevent alpha particles from penetrating deeply into matter. The dissipated energy can cause surface burns on the skin, but do no serious harm because alpha particles cannot reach internal organs. Alpha particles produced inside the body cause much greater damage because energy is deposited in the internal organs. This is how radon gas causes serious tissue damage. Beta particles have lower energy than alpha particles. Due to their smaller size/charge, most beta particles can pass several centimeters into the body. Due to its penetrating power, beta radiation is often more dangerous than that from alpha particles. While gamma particles can pass entirely though the body, depositing energy in the vital organs, causing damage. Figure 5: The possible health hazards from exposure to ionizing radiation depend on the penetrating power of the radiation. Ionizing and penetrating power must be considered when designing space-bound electronic devices. Computer chips and other solid-state devices rely on carefully controlled distributions of electrons and holes in semiconductor materials. Production of ions by ionizing radiation can cause catastrophic failure of electronic devices. The single event effect results when a single ionizing particle can produce large numbers of ions. For an instance, electronics in satellites are packaged in “hardened” materials to protect against cosmic rays. Methods of Detecting Radiation To assess radiation doses, the type and amount of radiation must be measured. The first measurements used a zinc sulfide phosphor, which produced tiny flashes of light when struck by radiation and the light flashes were counted manually. Also, a scintillation counter is used with a fluorescent screen to detect radiation, but the resulting photon strikes a phosphor that releases an electron instead of light flashes. A photomultiplier tube amplifies the electronic signal, producing a current pulse registered electronically. Another example is the Geiger counter. It is a portable detector used to measure radioactivity. A glass tube containing a gas at low pressure (0.1 atm) is coated on the inside with a metal that acts as a cathode. An anode wire runs down the center of the tube, and then a high voltage is applied across the electrodes. Alpha and beta particles enter through a window and ionize the gas atoms. The electrons released by the gas atoms are attracted to the anode, and ionize more gas as they travel to the anode, releasing more electrons. When the avalanche of electrons reaches the anode, a current pulse is recorded. Figure 6: In a Geiger-Mueller tube, radiation passes through a thin window into a gas-filled tube, producing ions in the gas. The resulting ions are attracted to oppositely charged electrodes, producing a pulse of electric current. A film-badge dosimeter monitors the radiation exposure for people who work with radioactive isotopes. Radiation darkens photographic plates. The darkened badge and a record of exposure provides a warning mechanism if safety levels are exceeded. All measurement methods must take background radiation into account when making measurements. Cosmic rays and natural radioactive isotopes in soil, air, and water are sources of background radiation. Background radiation must be subtracted from measurements of radioactive sources. Measuring Radiation Dose The interplay between ionizing power and penetrating power result in a number of different ways to express radiation dose. The quality factor, Q, is used to calculate the equivalent dose and is also known as the relative biological effectiveness (RBE). The value of Q varies from a value of one for high-energy photons to about 20 for alpha particles.  Table 2: Definitions and Units used to Quantify Exposure to Radiation Modern Medical Imaging Methods Modern imaging methods include the use of radioisotopes to obtain images of specific organs and elaborate techniques such as positron emission tomography (PET). During an X-ray, X-ray radiation passes through the body and a photographic image is produced based on the amount of radiation absorbed. Bone absorbs X-rays more strongly than organs or other tissues, and is an excellent orthopedic diagnostic tool. X-rays can also be used to examine the structure of some organs, such as a chest X-ray to examine the lungs or heart. The function of organs can be examined by selectively introducing small amounts of an appropriate radioisotope into the target organ. Radiation from the isotope is monitored to produce a detailed image of the organ. Structure, as well as function, can be revealed. The radioactive isotopes are introduced into target organs by taking advantage of biochemistry. Certain atoms and compounds are taken up specifically by particular organs. The thyroid gland uses iodine to produce thyroid hormone. Radioactive 131I is introduced and carried to the thyroid via natural biochemical pathways. In the thyroid, the 131I undergoes beta decay. Detection of the gamma particles produces an image of the thyroid gland. The procedure is extremely safe because the radiation dose is fairly small and the half-life of the isotopes is not too long. PET images are based on isotopes that emit positrons. Neutron-deficient isotopes tend to emit positrons. Available positron emitters are 11C, 18F, 13N, and 15O. These elements are found in common organic molecules, allowing for easy incorporation into appropriate biological molecules. Each decay of the radioisotope releases a positron. Positrons have extremely short lifetimes in the body. It travels no more than a couple of millimeters before encountering an electron. The positron and electron undergo matter-antimatter annihilation. The positron-electron annihilation produces two gamma rays 180 degrees apart. Detectors register the gamma rays, and computers map out the path taken by the tagged compounds. The result is a map of a slice through the body. Figure 7. Positron emission tomography (PET) produces high-quality images of the brain and other organs.  References Brown L, Holme T. (2011). Chemistry for Engineering Students. Mary Finch. https://ionlights.keybase.pub/books/Chemistry%20for%20Engineering%20Students%2C%202e.pdf Jain J. (2015). Engineering Chemistry. Dhanpat Rai. https://pdfcoffee.com/engineering-chemistry-by-jain- amp-jain-pdf-free.html