Nuclear Chemistry The nuclei of some unstable isotopes change by releasing energy and particles, collectively known as radiation Spontaneous nuclear reactions - five kinds: ) Emission of α-particles: 4 2He (helium nucleus) e.g. 238 92 U 234 90 Th + 4 2 He In air, α-particles travel several cm. In Al, α-particles travel 0-3 mm. 2. Emission of β-particles: 0 e (= electron) e.g. 3 53 I 3 54 Xe + 0 e β-emission converts a neutron to a proton: 0 n p + e In air, β-particles travel 0m. In Al, β-particles travel 0.5mm. 3. Emission of γ-rays: 0 0 γ γ-ray emission changes neither atomic number nor mass. In Al, γ -particles travel 5-0 cm.
4) Emission of positrons (= anti-electron, or β + -particle): 0 + e e.g. 6 C 5 B + 0 e Positron emission converts a proton to a neutron: p 0 n + 0 e Positrons have a short lifetime because they recombine with electrons and annihilate: 0 e + 0 e 2 0 0 γ 5) Electron Capture: an electron from the orbitals near the nucleus can be captured: e.g. 8 37 Rb + 0 e 8 36 Kr Electron capture converts a proton to a neutron: p + 0 e 0 n 2
239 94 Pu 4 2He +? Fill in the blanks 234 9 Pa 234 92U +?. p 2. 0 e 3. 0 n 4. 4 2 He 92 77 Ir +? 92 76Os 8 9 F 8 8O +? Sources of Exposure to Radiation Average annual exposure (mrem) 00 50 Radon 200 mrem (55%) Rocks and Soil 28 mrem (8%) Natural Cosmic Rays 27 mrem (8%) Radioisotopes in the body 39 mrem (%) Medical X-rays 40 mrem (%) Anthropogenic Nuclear medicine 4 mrem (4%) Consumer products mrem (3%) Source 3
NUCLEAR DECAY KINETICS Because the mechanism is unimolecular, nuclear decay is always a first order process. Decay Rate = -dn/dt = kn where: k is a constant, N is the number of decaying nuclei. Integrated rate law: ln[n(t)/n 0 ] = -kt N(t) = N 0 e -kt where N 0 is the number of radioactive nuclei at t=0. Half-Life: the time required for half of a radioactive sample to decay. Examples: N(t /2 ) = N 0 /2 ln(n/n 0 ) = -kt Half-Life k = 0.693/t /2 ; t /2 = 0.693/k Isotope t /2 Decay 238 92 U 4.5x0 9 yr α 235 92 U 7.x0 8 yr α 4 6 C 5.7x0 3 yr β 4
Strontium-90, which is a fission product of uranium, has a half-life of 28 years. This isotope is a significant environmental concern. What fraction of 90 Sr produced today will remain after 00 years? Radiocarbon Dating Libby (946) developed method of determining age using 4 6C. 4 6 C is produced by cosmic radiation. 4 7 N + 0 n 4 6 C + H 7.5 kg/year (~constant) It decays: 4 6 C 4 7 N + - e t /2 = 5.73 x 03 years Initially, in live plant C-4 has 4 dpm of C (dpm = disintegrations/min/g) When the plant dies, the C-4 is not replaced and the disintegrations diminish. Ex. The dead sea scrolls have dpm. What is the age of the document? 5
NUCLEAR STABILITY Rules: ) Up to atomic number 20, n=p is stable. 2) Above atomic number 20, n>p is stable. 3) Above atomic number 84, all nuclei are unstable. 4) Nuclei with 2, 8, 20, 28, 50, or 82 protons, or 2, 8, 20, 28, 50, 82, or 26 neutrons are particularly stable. These are the nuclear equivalent of closed shell configurations (and are called magic numbers). 5) Even numbers of protons and neutrons are more stable. # of Stable Nuclei With This Configuration: # Protons # Neutrons 57 Even Even 52 Even Odd 50 Odd Even 5 Odd Odd NUCLEAR STABILITY An isotope that is off the belt of stability can use four nuclear reactions to get to it:. α 2. β 3. positron emission 4. electron capture 6
NUCLEAR STABILITY An isotope with a high n/p ratio is proton deficient. To convert neutrons to protons, it can undergo β-decay: 0 n p + 0 e e.g. 97 40 Zr 97 4 Nb + 0 e NUCLEAR STABILITY contd. An isotope with a low n/p ratio is neutron deficient. To convert protons to neutrons, there are two possibilities: i) Positron emission: p 0 n + 0 e e.g. 20 Na 20 0 Ne + 0 e ii) Electron capture: p + 0 e 0 n Elements with atomic numbers greater than 84 undergo α-decay in order to reduce both the numbers of neutrons and protons: e.g. 235 92 U 23 90 Th + 4 2 He 7
238 U DECAY Cascade of α and β decay reactions Moves diagonally down belt of stability Eventually gets to stable isotope ( 206 Pb) 8
NUCLEAR BINDING ENERGY 2 p + 2 0 n 4 2 He p mass is.00728 amu 0 n mass is.00867 amu 4 2 He mass is 4.0050 amu Mass defect = (2)(.00728 amu) + (2)(.00867 amu) 4.0050 amu = 0.03040 amu = 5.047x0-29 kg Binding energy is the energy required to decompose the nucleus into nucleons (p and n): E = mc 2 Probably better to write: ΔE = (Δm)c 2 ΔE = (5.047x0-29 kg) (3x0 8 m/sec) 2 NUCLEAR BINDING ENERGY contd. ΔE = (5.047x0-29 kg) (3x0 8 m/sec) 2 = 4.543x0-2 J/ 4 2 He = 2.736x0 2 J/mole 4 2He (huge compared to ΔE for chemical reaction) Binding energy per nucleon: 4 2 He:.4x0-2 J 56 26 Fe:.4x0-2 J (largest - most stable nucleus) 238 92 U:.22x0-2 J Nuclei with mass greater than ~200 amu can fall apart exothermically nuclear fission. Combining light nuclei can be exothermic nuclear fusion. 9
The rest masses of proton, neutron, and 2 C nuclei are: p =.007276470 amu n =.008664904 amu 2 6 C = 2 amu (exact) Practice problem: (a) Calculate the binding energy/mole of 2 C. (b) Calculate the binding energy/nucleon. (c) Compare to ΔE for combustion of one mole C. 0
Fission NUCLEAR CHAIN REACTIONS 235 92 U + 0 n 37 52 Te + 97 40 Zr + 2 0 n 42 56 Ba + 9 36 Kr + 3 0 n An average of 2.4 neutrons are produced per 235 U. Chain reactions: Small: Medium: Large: most neutrons are lost, subcritical mass. constant rate of fission, critical mass, nuclear reactor. increasing rate of fission, supercritical mass, bomb. CRITICAL MASS
NUCLEAR REACTORS Nuclear reactor fuel is 238 U enriched with 3% 235 U. This amount of 235 U is too small to go supercritical. The fuel is in the form of UO 2 pellets encased in Zr or steel rods. Liquid circulating in the reactor core is heated and is used to drive turbines. This liquid needs to be cooled after use, so reactors are generally near lakes and rivers. NUCLEAR REACTORS Cadmium or boron are used in control rods because these elements absorb neutrons. Moderators are used to slow down the emitted neutrons so that they can be absorbed by adjacent fuel rods. 2
Nuclear Fission Bombs Mainly U-235. Fortunately, U-235 is hard to purify Uranium ore is concentrated and treated with Fluorine to form UF 6. This is low boiling and can be evaporated at 56 o C. 99.3% is non-fissionable U-238. Chemical reactions don t help separate isotopes. Gaseous diffusion separates the heavier particles (UF 6 with U-235 moves 0.4% faster than U-238) Repeated diffusion over long barriers or centrifugation concentrates U-235 Breeder reactors- 238 U + n 239 Pu + 2e. Under Glenn Seaborg, Plutonium bomb was produced at Hanford, WA. Plutonium can be used for bombs or as a fuel source. However, small amounts of PuO 2 dust in air causes lung cancer. Very toxic. Breeder Reactors Breeder reactors are a second type of fission nuclear reactor. A breeder reactor produces more fissionable material than it uses. 239 94 Pu and 233 92U are also fissionable nuclei and can be used in fission reactors. 238 92 U + 0 n 239 92 U 239 93 Np + 0 e 239 94 Pu + 0 e 232 90 Th + 0 n 233 90 Th 233 9 Pa + 0 - e 233 92 U + 0 - e 3
NUCLEAR REACTORS Fusion Chemistry of the stars The sun contains 73% H, and 26% He. H + H 2 H + 0 + e H + 2 H 3 2 He 3 2 He + 3 2 He 4 2 He + 2 H 3 2 He + H 4 2 He + 0 e Initiation of these reactions requires temperatures of 4x0 7 K - not currently obtainable on a stable basis. Nuclear Fusion Tremendous amounts of energy are generated when light nuclei combine to form heavy nuclei-sun (plasma ~0 6 K) Short range binding energies are able to overcome the proton-proton repulsion in the nuclei 2 H + 2 0 n 4 2 He ΔE= -2.73 x 0 2 J/mol Binding energy = +2.5 x 0 8 kj/mol Note: (covalent forces are only are fraction H-H bond E =436 kj/mol) The huge energy from 4 g of helium could keep a 00 Watt bulb lit for 900 years 4
H-bomb 6 3 Li + 0 n 3 H + 4 2 He ΔE= -.7 kj/mol/ mol tritium The nucleons combine in a high energy plasma (~0 6 K). A U-235 or Pu-239 bomb is set off first. A 20- megaton bomb has 300 lbs Li-D as well as a fission/atomic bomb. 5