radioactivity: a spontaneous (naturally-occurring) emission of particles or radiation from the nuclei of atoms
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1 CHAPTER 20: Atomic Structure Nuclear Chemistry radioactivity: a spontaneous (naturally-occurring) emission of particles or radiation from the nuclei of atoms Historical Background Roentgen (1895) discovery of x-rays Fluorescence of rocks and minerals (uv light source) Becquerel (1896) radiation from pitchblende ore, but without prior irradiation Principal Radiation Types (nuclear decay process) Alpha particles (α) Beta(-) rays or particles (β(-)) Gamma rays (gamma radiation) (γ) Atomic nuclei undergo decay when they are unstable. Stable nuclei do not undergo any type of change (decay). Types of Radioactivity: Alpha, Beta(-), Gamma Radiation Type Mass (a.m.u.) Charge Description Alpha, a He 2+ Beta(-),ß high-energy electron Gamma,? 0 0 pure energy Relative Penetrating Power of Alphas, Betas and Gammas The Alpha Decay Process: Example of an Alpha Decay 210 Po 84 4 He Pb Po 84 = parent isotope and 206 Pb 82 = daughter isotope Note that the mass number decreases by 4 and the atomic number decreases by 2 for an alpha decay, producing a daughter element with an atomic number 2 less than the original parent isotope.
2 The Beta(-) Decay Process: Example of a Beta(-) Decay 14 C 6 0 e N 7 14 C 6 = parent isotope and 14 N 7 = daughter isotope Note that the mass number remains unchanged and the atomic number increases by 1 for a beta(-) decay, producing a daughter element with an atomic number 1 more than the original parent isotope. This process converts a neutron to a proton. Decay by Electron Capture ( K-capture ) Example of Decay by Electron Capture 7 Be e Li 3 7 Be 4 = parent isotope and 7 Li 3 = daughter isotope Note that the mass number remains unchanged and the atomic number decreases by 1 for K- capture, producing a daughter element with an atomic number 1 less than the original parent isotope. This process converts a proton to a neutron. Example of Decay by Beta(+)(or Positron) Decay.. competes with Electron Capture 207 Po 84 0 e Bi Po 84 = parent isotope and 207 Bi 83 = daughter isotope Note that, again, the mass number remains unchanged and the atomic number decreases by 1 for a beta(+) decay, producing a daughter element with an atomic number 1 less than the original parent isotope. This process also converts a proton to a neutron. Stability of Atomic Nuclei Why are some nuclei stable and others unstable? We should have some feel for this since we have already seen some isotopes that are unstable and that undergo decay by processes that 1. convert neutrons to protons (β(-)) 2. convert protons to neutrons (β(+) and K-capture) The Band of Stability and Radioactive Decay Consider a plot of # of neutrons versus # of protons for isotopes of atoms from Z=1 to Z=83 Except for H and He, stable isotopes have mass numbers (A) that are always at least 2 times as large as their atomic numbers (Z)... at least 1 neutron for every proton.
3 1. Light elements have equal numbers of protons and neutrons (up to Ca) 2. n/p ratio increases with increasing Z 3. Above bismuth (Z=83) all isotopes are unstable 4. Even Z elements have more stable isotopes than odd Z A shell model for nuclei? Shell Model of the Nucleus Protons and neutrons in atoms exist in shells or energy levels with the total number of protons in shells having special stabilities associated with them Nuclei with certain numbers of neutrons or protons appear to be stable -- these numbers are called magic numbers For protons, magic numbers include: 2, 8, 20, 28, 50, 82 and 114 For neutrons, magic numbers include: 2, 8, 20, 28, 50, 82 and 126 Example of a stable nucleus: Pb-82 When Z > 83, no stable nuclide exists -- proton-proton repulsions become too large. Binding Energy Per Nucleon The stabilization energy of a nucleus, divided by the number of protons and neutrons it has, is the binding energy per nucleon. The greater the binding energy, the more stable the nucleus The most stable nuclei are in the range from A = Mass Defect and Binding Energy Where does the binding energy come from? Actual mass of atoms is always less than the sums of the masses of electrons and nucleons that it contains. Loss of mass occurs during atom s formation of atom s nucleus from protons and neutrons.. DE = Dmc 2 m = mass defect of the nucleus (energy lost) E = energy equivalent of mass (binding energy) The more energy that is lost, the more stable the resulting nucleus... Very light nuclei (like H and He) and very heavy nuclei (like U and Pu) are unstable (low binding energies); light nuclei combine (fusion), while very heavy nuclei split apart (fission). The most stable nuclei are in the range from A = 50-80; Fe-56 most stable Decay by Electron Gamma Emission In gamma decay, a nucleus changes from a higher energy state to a lower energy state through the emission of electromagnetic radiation ( photons ). Since the number of protons and neutrons in the nucleus does not change, parent and daughter atoms are the same chemical element.
4 In the gamma decay, the emitted photon (gamma ray) and the nucleus divide the energy between only two particles. During a gamma decay, the excited nucleus is stabilized by releasing excess energy in the form of pure radiant energy (a gamma ray, g). Gamma rays are more powerful (and more penetrating) than x-rays. Another Example of Gamma Decay 137 mba 56 * γ Ba mba 56 = parent isotope and 137 Ba 56 = daughter isotope Here, both the mass number and the atomic number remain do not changed, producing a daughter atom that has lost excess energy in the form of a gamma ray. Rates of Nuclear Decay Processes activity: number of disintegrations per second occurring in a radioactive sample Units of radioactivity: SI: 1 becquerel (Bq) = 1 disintegration/second Old unit: Curie (Ci), where 1 Ci = 37 billion Bq = rate of disintegration for 1 gram of radium (Ra) Radioactive decay is a first-order kinetic process... A = kn where A = activity N = # radioactive atoms k = decay constant Half-life (t 1/2 ) : the time required for half of a radioactive sample to undergo decay from parent to daughter isotope: t 1/2 = 0.693/k To find the fraction of radioactive material remaining after n half lives, raise ½ to the n th power Ex. What fraction of a radioactive sample remains after 3 half lives? Answer: (1/2)3 = ½ x ½ x ½ = 1/8 Half-Life Carbon-14 has a half-life of about 5700 years, while tritium (H-3) has a half-life of about 12 years. What happens if we start out with 32 lb of radioactive H-3? 32 lb 16 lb 8 lb 4 lb 2 lb (1/16) 12 yr 12 yr 12 yr 12 yr What fraction remains after 48 years? 48 years x (1 half-life/12 years) = 4 half-lives fraction remaining = ½ x ½ x ½ x ½ = = 1/16
5 Rate of Nuclear Decay First order decay processes are logarithmic decays No. Radioactive Atoms versus Time # Atoms Days Practice Problems for Half-Life What fraction of a radionuclide remains and what fraction has decayed after one half life? (½ and ½) two half lives? (½ x ½ =1/4 and 1 ¼ = ¾) three half lives? (½ x ½ x ½ = 1/8 and 1 1/8 = 7/8) Half-Life For materials with very short half-lives, we observe that they disappear (are converted to daughter isotopes) very quickly: but, 214 Pb Bi e -1 t 1/2 = 26.8 min 218 At Bi He 2 t 1/2 = 1.3 s 238 U Bi He 2 t 1/2 = 4.5 billion yr When element 104 was synthesized, only 3000 atoms were made. The half-life for element 104 is 4.5 seconds. How many atoms remained after 4.5 seconds? Solution: half-lives = (4.5 s)(1 half-life/4.5 s) = 1 half-life) atoms = (1/2) (3000) = 1500 atoms left after 9.0 seconds? half-lives = ((9.0 s)(1 half-life/4.5 s) = 2 half-lives atoms = (1/2) x (1/2) (3000) = 750 atoms left Many Radioactive Materials Occur Naturally: Examples C-14 (~ 15 disintegrations/s in human bodies) K-40 (~ 15 disintegrations/s in human bodies) Sr-90 (food); Cs-137 (food); Rn-222 (as gas in air) All of these and more are contributors to our natural exposure background radiation. Longterm effects not known
6 Cosmic Radiation Penetrating ionizing radiation, both particulate and electromagnetic, originating in outer space. Secondary cosmic rays, formed by interactions in the earth's atmosphere, account for about 45 to 50 mrem of the 360 mrem background radiation that an average individual receives in a year. Radiological Dating Radiocarbon dating (up to 50,000 years old) uses C-14 Radiocalcium dating Tritium dating (up to 100 years)
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