Nuclear Chemistry Chapter 23 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. PowerPoint Lecture Presentation by J. David Robertson University of Missouri

X A Z Mass Number Atomic Number Element Symbol Atomic number (Z) = number of protons in nucleus Mass number (A) = number of protons + number of neutrons = atomic number (Z) + number of neutrons A Z 1p1p 1 1H1H 1 or proton 1n1n 0 neutron 0e0e 00 or electron 0e0e +1 00 or positron 4 He 2 44 2 or  particle

Balancing Nuclear Equations 1.Conserve mass number (A). The sum of protons plus neutrons in the products must equal the sum of protons plus neutrons in the reactants. 1n1n 0 U Cs Rb n1n = x1 2.Conserve atomic number (Z) or nuclear charge. The sum of nuclear charges in the products must equal the sum of nuclear charges in the reactants. 1n1n 0 U Cs Rb n1n = x0 23.1

212 Po decays by alpha emission. Write the balanced nuclear equation for the decay of 212 Po. 4 He 2 44 2 or alpha particle Po 4 He + A X 84 2Z 212 = 4 + AA = = 2 + ZZ = Po 4 He Pb

Nuclear Stability and Radioactive Decay Beta decay 14 C 14 N + 0  K 40 Ca + 0  n 1 p + 0  Decrease # of neutrons by 1 Increase # of protons by 1 Positron decay 11 C 11 B + 0  K 38 Ar + 0  p 1 n + 0  Increase # of neutrons by 1 Decrease # of protons by 1 and have A = 0 and Z =

Electron capture decay Increase # of neutrons by 1 Decrease # of protons by 1 Nuclear Stability and Radioactive Decay 37 Ar + 0 e 37 Cl Fe + 0 e 55 Mn p + 0 e 1 n Alpha decay Decrease # of neutrons by 2 Decrease # of protons by Po 4 He Pb Spontaneous fission 252 Cf In n

n/p too large beta decay X n/p too small positron decay or electron capture Y 23.2

Nuclear Stability Certain numbers of neutrons and protons are extra stable n or p = 2, 8, 20, 50, 82 and 126 Like extra stable numbers of electrons in noble gases (e - = 2, 10, 18, 36, 54 and 86) Nuclei with even numbers of both protons and neutrons are more stable than those with odd numbers of neutron and protons All isotopes of the elements with atomic numbers higher than 83 are radioactive All isotopes of Tc and Pm are radioactive 23.2

Nuclear binding energy (BE) is the energy required to break up a nucleus into its component protons and neutrons. BE + 19 F 9 1 p n BE = 9 x (p mass) + 10 x (n mass) – 19 F mass E = mc 2 BE (amu) = 9 x x – BE = amu 1 amu = 1.49 x J BE = 2.37 x J binding energy per nucleon = binding energy number of nucleons = 2.37 x J 19 nucleons = 1.25 x J 23.2

Nuclear binding energy per nucleon vs Mass number nuclear binding energy nucleon nuclear stability 23.2

Kinetics of Radioactive Decay N daughter rate = - NN tt rate = N NN tt = N - N = N 0 exp(- t)lnN = lnN 0 - t N = the number of atoms at time t N 0 = the number of atoms at time t = 0 is the decay constant ln2 = t½t½ 23.3

Kinetics of Radioactive Decay [N] = [N] 0 exp(- t) ln[N] = ln[N] 0 - t [N] ln [N] 23.3

Radiocarbon Dating 14 N + 1 n 14 C + 1 H C 14 N + 0  t ½ = 5730 years Uranium-238 Dating 238 U 206 Pb   t ½ = 4.51 x 10 9 years 23.3