Key Worksheet 21 Nuclear Chemistry Objectives To be able to write and use a nuclear chemical equation. To be able to predict the missing reactants or products in a nuclear chemical reaction. To be able to use the integrated rate law for nuclear decay. To be able to use Einstein s mass/energy equation to calculate mass defect or energy released during a nuclear reaction. Alpha Particle: or Beta Particle: or Neutron: or n 0 Positron: Proton: or p + Gamma Ray: Neutron: 1.67493 x 10 24 g Proton: 1.67262 x 10 24 g Electron: 9.10939 x 10 28 g 1.) Write a nuclear equation describing each of the following. Electron Capture by 68 Ga Alpha Decay of 212 Fr Positron Emission of 62 Cu Beta Emission of 129 Sb Page 1 of 6
2.) The isotope 247 Bk undergoes a series of and decays, ending up as 207 Pb. Overall during this process how many particles and how many particles are produced? Since the only process that will change the mass number for this decay is alpha emission, we can figure out the number of alpha particles by looking at the difference in mass numbers and dividing by 4: 247 207 = 40, 40/4 = 10. We know the atomic number has change by +20 from the alpha decay (2 x 10), The actual change in atomic number is 97 82 = 15. That means 5 beta particles must have been emitted since each beta particle subtracts 1 from the overall atomic number. # particles = 10 3.) Complete each of the following equations. # particles = 5 a.) 73 Ga 73 Ge + b.) 60 Co 60 Ni + c.) 192 Pt 188 Os + d.) 97 Tc + 97 Mo e.) 205 Bi 205 Pb + f.) 99 Tc 99 Ru + g.) 239 Pu 235 U + h.) 241 Cm + 241 Am i.) + 243 Bk + n 0 j.) 238 U + 12 C + 6 n 0 k.) 249 Cf + 260 Db + 4 n 0 l.) 249 Cf + 10 B 257 Lr + 4.) The half life of 241 Am (used in smoke detectors) is 433 years. How many particles are emitted each second by a 3.50 g sample of 241 Am? (The particles ionize smoke particles which are detected by a charged particle detector). First use the half life to find the rate constant, k: Now we multiply this by the number of nuclei to get the number of particles per second (converting units along the way). # particles = 4.44 x 10 11 Page 2 of 6
5.) The first atomic bomb was detonated in the desert by Alamogordo, New Mexico, on July 16, 1945. 90 Sr (t 1/2 = 28.9 years) was one of the products of the nuclear reaction. What fraction of the 90 Sr produced originally in that explosion remains today? First use the half life to find the rate constant: Now use the integrated rate law to find the fraction remaining (assuming today is April 2, 2018): Fraction 90 Sr Remaining = 0.177 6.) The isotope 82 Br has a half life of 1.0 x 10 3 minutes. If you needed 2.5 grams of 82 Br and you buy it in the form of Na 82 Br, what mass of Na 82 Br should you order if it takes 4.5 days for it to get to you? First use the half life to find the rate constant: Next find the fraction remaining after 4.5 days (converting the 4.5 days to minutes): Mass Na 82 Br = 290 g Page 3 of 6
7.) Given that the ratio of 14 C/ 12 C 13.6 counts per minute per gram living matter remains constant, if a fossil is found to have 0.95 counts per minute per gram how old is the fossil? The half life of 14 C = 5730 years. Age of Fossil = 22,000 years 8.) Calculate the binding energy per nucleon for 93 Nb (isotopic mass =92.9063730 g/mol). First calculate the mass of components, then find the difference in mass of the components and the atom ( m). Now find the binding energy per nucleus, then per nucleon. Binding Energy = 1.4 x 10 12 J/nucleon Page 4 of 6
9.) The binding energy per nucleon for 27 Mg is 1.326 x 10 12 J/nucleon. Calculate the isotopic mass of 27 Mg. Now calculate the mass of the components. Now find the mass of an atom and then the mass of a mole of the atoms. Isotopic Mass 27 Mg = 26.98g/mol 10.) Calculate the amount of energy released per gram of hydrogen atom reacted when two hydrogen nuclei undergo a fusion reaction. The atomic mass of hydrogen 1 is 1.00782 amu, that of deuterium 2.01410 amu, and an electron is 0.00054858 amu. First find the difference mass between the reactants and the products. Note that the masses given include electrons, so we have to subtract the mass of the electrons to get the masses of the nuclei. m =(mass deuterium mass electron + mass positron ) 2(mass H 1 mass electron ) = (2.01410 amu) 2(1.00782 amu 0.00054858 amu) = 0.00044 2 amu The m in amu is the same value as the m in g (on a molar basis), so m = 0.00044 2 g = 4.4 2 x 10 7 kg Now we use Einstein s equation: Energy per g H = 2.0 x 10 10 J Page 5 of 6
11.) Calculate the energy per gram of particles produced in the following fusion reaction. The atomic mass of deuterium is 2.01410 amu, tritium is 3.01605 amu, helium 4 is 4.00260 amu, an electron is 0.00054858 amu, and a neutron is 1.00866 amu. First find the difference in mass between the reactants and products. Then convert to kg, and use Einstein s equation. Once more note that wee should subtract the mass of the electrons. Energy per gram of Particles = 4.242 x 10 11 J Page 6 of 6