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Nuclear Reactions Radioactive Decay The stability of an isotope depends on the ratio of protons and neutrons in the nucleus. If the ratio does not lie in the curve of stability (dots on the graph), the nucleus can undergo spontaneous radioactive decay. There are several different forms of decay, and an atom will usually go through a many decays on its way to stability. Radioactive Half-Life Every radioactive isotope decays at a different rate. The time it takes for half of the sample to decay is known as the half-life. e.g. Carbon-14 Half-life (T½) of carbon-14 = 5730 years. Starting with 1.0 g of carbon-14, in 5730 years, 0.50 g will be remaining. In 11460 years 0.25 g will remain. In 22920 years 0.0625 g will remain. Etc… Mathematically: mass remaining = initial mass * (½)n where n = time passed (t) ÷ half-life (t1/2) OR: Decay Types alpha decay (4α) 2 – the spontaneous emission of a helium nucleus from the atom 226 e.g. Ra → 222Rn + 4He These particles are easily blocked by a sheet of paper, but readily damage chromosomes if inhaled or ingested. beta decay (β-) - a neutron is converted into a proton and a beta particle (an electron created within the nucleus but otherwise indistinguishable from an orbital electron) 14 0 e.g. C → 14 -1 N + β gamma decay (0γ) – a gamma particle is a high energy photon which is emitted when 0 the nucleus is in an excited state. Gamma rays are dangerous because it is hard to block them, but this also makes them useful for medical diagnostics. Radioactive Emissions Mass Defect If you were to take any atom and separate it into its subatomic components (protons, neutrons, electrons) and weigh them, the sum of the masses of the components will be higher than when they were all together as an atom. This mass difference is called the mass defect. Violation of the law of conservation of mass? No! Due to Einstein’s famous equation, E=mc2, we know that the missing mass changed into energy to keep the atom together. The law of conservation of mass and the law of conservation of energy are the same conservation law. Mass and energy are still conserved, as they can be converted into each other. e.g. The mass of a proton is 1.0073 amu (atomic mass units) and a neutron is 1.0087 amu. This means that a helium nucleus (with 2 protons and 2 neutrons) should have a mass of 4.032 amu, but its actual mass is 4.0015 amu. E = mc2 E = energy (J), m = mass (kg), c = speed of light = 3.0 x 108 m/s For a large sample of helium that has a mass defect of 0.0305 g, E = (0.000 030 5 kg)( 3.0 x 108 m/s)2 = 2.75 x 1012 J was released when creating the atom! Mass Difference Atoms that are more stable require less energy to keep them together. By making atoms that are more stable from atoms that are less stable, the difference in energy can be released and used! The energy difference between the less stable atoms and the more stable atoms that are created is seen as a difference in mass, as according to E=mc2. Nuclear Fission By taking a large, unstable, atom and breaking it apart into two (or more) more stable atoms, the mass deficit (difference) will be positive and energy will be released. This is generally achieved when a neutron strikes an unstable nucleus, causing it to split apart. e.g. unstable Uranium-235 235 U + 1n → 92Kr + 141Ba + 3 1n + energy When U-235 is struck by a neutron, it produces 3 more neutrons which then can react with other uranium atoms creating a chain reaction that can produce massive amounts of energy in under a microsecond. This process is called Nuclear Fission, and is the principle being Nuclear Power. Canadian CANDU reactors use natural uranium (mostly U-238) but can also run on other radioactive materials, including plutonium taken from old nuclear weapons, and used fuel rods from other nuclear plant designs. CANDU reactors use heavy water (D2O – where D = 2H) to slow down neutrons so they can be more easily absorbed by the radioactive isotopes to initiate nuclear fission. 238 U + 1n → 239U → 239Np + β- → 239Pu + β- → 235U + 4He Nuclear Fusion By taking two (or more) smaller atoms and combining them into a large and more stable atom, the mass deficit (difference) will positive and energy will be released. This is called nuclear fusion. Nuclear fusion creates a larger difference in mass than nuclear fission, thus releases even more energy. Nuclear fusion is the process by which our sun (and all other stars) create their energy. e.g. the sun The sun consists of a series of layers where different nuclear fusion reactions take place. In the sun’s core, hydrogen atoms are combined to create helium atoms. 1 H + 1H → 2H + β + 2 H + 1H → 3He 3 He + 3He → 4He + 2 1H In other layers helium combine to form beryllium, beryllium combine with helium to form carbon and carbon combine with helium to form oxygen Iron is the most stable atom, so nuclear fission only releases energy for atoms larger than iron. Similarly, nuclear fusion can only occur up to element 26 (iron), but after this point, the amount of energy required to fuse the nuclei in stars is too large to be sustainable. This stops the reactions, in turn stopping the outward pressure from the gases formed, leading to a collapse of the star and finally a supernova. In a supernova, the pressure of the collapsing star generates the energy needed to produce all of the elements higher than iron. Example: fusion