Nuclear Chemistry Nuclear reactions are transmutation of the one element into another. We can describe nuclear reactions in a similar manner as regular chemical reactions using ideas of stoichiometry, kinetics, and thermodynamics to convert of an element into another nuclear species. Model : Stoichiometry of Nuclear Reactions Nuclear Reactions can be categorized as three general types: A. Radioactive Decay B. Fission Reactions C. Nuclear Transformation (or Fusion Reactions) For each of these reactions, three quantities are conserved: energy, nuclear charge, and baryon number (mass number). The topic of energy will be addressed in greater detail in the section on thermodynamics. A. Radioactive Decay Processes Decay processes are the general pathways for the decomposition of a nucleus. These processes may involve the ejection of a particle from the nucleus or the capture of a core electron by the nucleus. Each particle has a specific mass number (A) and charge (Z) associated with its symbol in the usual way: A ZX.; the particles emitted from a nucleus undergoing radioactive decay are: α particles are helium nuclei: 4 He + β particles are high-energy electrons: 0 -e β + particles are positrons, the anti-particles of electrons: 0 e + γ particles are high-energy photons: 0 0γ In addition, the final decay process, the capture of a core electron ( 0 -e ), proceeds by converting a proton within the nucleus into a neutron. Decay Reactions The most common form of nuclear decay reactions are the following: α decay emission of an α particle from the nucleus: 9 U xxv 4 He + + 3 90Th (note: the sum of the mass numbers ( = 3+4) and the nuclear charges (9 = +90) for the species are unchanged in the process) CTQ. Predict the products of the following reactions: β decay - emission of a β particle from the nucleus: 7 He xxv 0 -e + β + decay - emission of a positron (β + ) particle from the nucleus: 8 5 B xxv 0 e + + isomeric transition or IT : γ decay - loss of a γ particle: 34 7 Cl xxv 0 0γ + electron capture or EC: capture of a core electron of the atom by the nucleus 7 4 Be + 0 -e xxv
Nuclear Decay Series Heavier nuclei may undergo a series of decays until arriving at a stable isotope. The figure below shows the pathway for the conversion of radioactive Uranium-38 to the stable lead-06 nucleus. (Note: the emission of gamma-rays are not accounted for in this figure) The first step shows the loss of four (4) mass units and a loss of two protons from the nucleus therefore, the decay process is the emission of an alpha particle ( 4 α ). The second step shows no change in mass number, but an increase in atomic number therefore the decay process is the emission of a beta particle (¹ ₁β). CTQ. How many alpha particles are produced as one mole of 38 U decays to 06 Pb How many beta particles? CTQ 3 When protactinium-9 goes through two alpha decays, francium- is formed. Write the two reactions below. CTQ 4 Write the nuclear reactions for the decay of Po-0 if it undergoes consecutive alpha decay followed by a beta decay followed by another alpha decay.
CTQ 5 Thorium-3 undergoes radioactive decay until a stable isotope is reached. Write the reactions for the decay of Th-3. There are eleven steps beginning with Alpha decay with each product becoming the reactant of the next decay. Circle the final Stable isotope. B. Nuclear Fission A fission reaction occurs when a heavy nucleus splits into two nuclei with smaller mass numbers; virtually all of these processes have the capture of a neutron by the heavy nucleus as an initiating step. For example, one pathway for the fission of Uranium- is: 37 97 5Te + 40Zn + 0 n This is only one of the observed pathways over 00 different isotopes of 35 different elements have been observed in the fission products of U. CTQ 6 Balance the following fission reactions: 4 56Ba + + 0 n 37 55Cs + + 3 0 n 39 + 94Pu 03 + 40Zr + 3 0 n 4 54Xe + + 3 0 n 36 00 4Mo 6 + 50Sn + 0 n
C. Nuclear Transformation (Fusion) Both fusion and nuclear transformation processes occur by the collision of two nuclei to form a heavier nucleus. The difference between the two types of processes is relative stability of the product. For the fusion reaction, the resultant nucleus is generally more stable than the reactants; for nuclear transformation, the resultant nucleus may be stable for only microseconds before undergoing radioactive decay. Example: nuclear synthesis of Seaborgium 63 8 8O 49 + Cf 98 63 06Sg CTQ 7: Balance the following fusion/transformation reactions: + 4 0 n H 5 + 7 N 4 He + H 3 + H 4 He + 6C 38 + 6 0 n 49 98Cf 0 + 5 B + 0 n Model Kinetics of Nuclear Decay All spontaneous nuclear decay processes are st order. This makes it convenient to discuss the kinetics in terms of half-lives and activity (the number of decays per second). For example, the half-life of 4 Am is 43 years, or.364 0 0 s. From the relation between the rate constant and half-life of a st order reaction ( k τ ½ = ln ), the rate constant for the decay of 4 Am is k = 5.08 0 s. From the rate law, we can determine the activity of a radioisotope, that is, the number of decays, from a mass of w grams of 4 Am (4.0568 amu). This is usually expressed in terms of Curies ( Ci = 3.70 0 0 s ) the number of decay events per second for gram of radium. Activity = Δ N Δ t = k N = k w M N A where M is the atomic mass OR Activity = k w M N A C i 3.70 0 0 s CTQ 8: Show that the specific activity (the activity per gram) of americium-4 is 3.43 Ci/g Am
CTQ 9: What mass of Na 38 SO 4 has an activity of 0.0 mci? Sulfur-38 has an atomic mass of 38.0 and a half-life of 4.5 days. How long does it take for 99.99% of the sample of sulfur-38 to decay? Model 3 Thermodynamics of Nuclear Reactions Mass Defect Consider a nucleus of carbon-: six protons, six neutrons, with a mass of exactly amu. However, consider the following information: mass of p =.0078 amu ; mass of 0 n =.00866 amu Expected mass of Actual mass of 6 C =.09564 amu C 6 =.00000 amu Mass lost in formation of 6 C nucleus = 0.09564 amu =.588 0 8 kg Although the mass change may be small, the corresponding energy change are large. Nuclear energy changes are related to changes in mass through a familiar relation: E = mc Δ E = (Δ m)c m mass measured in kilograms c speed of light =.998 0 8 meters seconds E Energy measured in Joules ( J = kg m sec ) For C: E =.588 0 8 kg atom (.9979 m 08 sec) =.473 0 J atom = 8.5957 0 J mole C
Nuclear Binding Energies As a nucleus is formed, mass is converted to energy; this energy loss is the stabilization of the nucleons (protons and neutrons) within the nucleus. The binding energy is defined as the amount of energy determined from the mass lost divided by the number of nucleons. For the next set of CTQ's, consider a single 9 F atom: CTQ 0: Given the mass of a proton is.007765 amu and the mass of a neutron is.0086649 amu, determine the expected mass of a 9 F atom. CTQ : The experimentally determined mass of the fluorine-9 nucleus is 8.998403amu; what is the mass lost as the nucleus forms? CTQ : Determine the energy which corresponds to this loss of mass for one nucleus. CTQ 3: Determine the energy which corresponds to this loss of mass for one mole of nuclei. CTQ 4: Determine the binding energy for F-9 per nucleon. One useful unit of energy used in nuclear processes is the electron volt (ev). It is the amount of kinetic energy an electron gains as it accelerates between two charged plates separated by cm with a volt difference on the plates. ev is.60766 0 9 J; in more familiar terms, ev corresponds to 96.485 kj/mol.
CTQ 5: Show that the binding energy of Iron-56 ( 55.9349 amu) is 8.5537 MeV per nucleon. Energies of nuclear reactions: Fission CTQ 6: Determine the energy which corresponds to this loss of mass for one mole of nuclei. One reaction in nuclear reactors is: n + U 36 U 9 Kr + 4 Ba + 3 n Given the following masses, determine the energy available from this process in kj/mol. Isotope Atomic Mass (amu) n.00866 U.0439 9 Kr 90.934 4 Ba 4.964 Fusion CTQ 7: The easiest fusion reaction to initiate is: H + 3 H 4 He + n Calculate the energy released per nucleus of 4 He produced and per gram of 4 He produced. Isotope Atomic Mass (amu) n.00866 H.040 3 H 3.0605 4 He 4.0060