Nuclear Reactions Fission and Fusion

artificial (induced) transmutation Change of one element into another through bombardment of the nucleus Nitrogen gas hit w/ alpha particles (Rutherford, 1919) Determined to produce O & H (Blackett, 1925) O-16 hit w/ neutrons

nuclear reaction equations Written in the form of a chemical equation Balance mass numbers Balance atomic numbers

unified mass unit Also called “Atomic Mass Unit” Exactly 1/12th the mass of a carbon 12 atom 1 u = 1.661  10-27 kg We need to be careful to distinguish between the atomic mass and the nuclear mass. The atomic mass is the mass of an atom complete with its electrons The nuclear mass is the mass of the nucleus alone. To get the nuclear mass we need to take away the mass of the electrons.

unified mass unit Particle Mass (u) Electron 0.000549 Neutron 1.008665 Proton 1.007276 Hydrogen atom (1p+ + 1 e-) 1.007825 Helium atom (2p+ + 2 n + 2e-) 4.002063 α particle (2p+ + 2 n) 4.001505

Einstein’s mass-energy equivalence relationship E = mc2 Joules = Kilograms (m/s)2 Used to calculate: Rest energy of a mass A mass not moving & has no additional energy due to work done on it Energy released in nuclear reactions

Einstein’s mass-energy equivalence relationship Must convert the mass from u to kg Energy calculated is in Joules. Joules not convenient @ nuclear level convert to electron volts (eV) divide by 1.6  10-19 J/eV A useful conversion factor between mass and energy is that 1 u = 931.3 MeV

mass defect The total mass of the nucleus is less than the sum of the mass of the individual neutrons and protons that formed the nucleus. The difference in mass is equivalent to the energy released in forming the nucleus.

He mass defect Particle Mass (u) # Total (u) 2 Electron 0.000549 2 0.001098 Neutron 1.008665 2.017330 Proton 1.007276 2.014552 4.032980 the atomic mass is 4.002603 u difference of 0.030377 u difference between the total mass of the nucleons and the measured mass of the nucleus

mass defect So with our helium atom, the missing 0.030377 u is released when the nucleons come together. That energy has to be put back to split the nucleus up again.

binding energy neutrons and protons held together by 'strong force'. acts over very small distances able to overcome the electrostatic repulsion between protons most tightly bound nuclei are those close to iron in the periodic table tightness of this binding is measured by the binding energy per nucleon also sometimes called the mass defect per nucleon

graph of binding energy The binding energy of atomic nuclei plotted against the atomic number of the nuclei. Energy is released by the fusion of light elements into heavier elements (elements on the left) or the fission of heavy elements into lighter elements (elements on the right).

graph of binding energy From this graph we can see the following: The vast majority of nuclides have a binding energy of 8 MeV per nucleon. Helium has a particularly high value of binding energy per nucleon, much higher than the light isotopes of hydrogen. There is a trend for nuclides of nucleon numbers in multiples of 4 to be particularly stable (i.e. have a high binding energy). Fe is the most stable nuclide. The largest nuclides tend to be less stable, with slightly lower binding energies per nucleon.

graph of binding energy Higher = more stable Iron is the highest element on the graph, and the most stable. It cannot release energy through either fusion or fission.

graph of binding energy most tightly bound nuclei are those close to iron in the periodic table of elements tightness of this binding is measured by the binding energy per nucleon sometimes called the mass defect per nucleon.

graph of binding energy general decrease in binding energy beyond iron is caused by the fact that, as the nucleus gets bigger, the ability of the strong force to counteract the electrostatic force between the protons becomes weaker peaks in binding energy at 4,8,16 and 24 nucleons is a consequence of the great stability of helium-4 a combination of two protons and two neutrons.

graph of binding energy The maximum binding energy at iron means that elements lighter than iron release energy when fused. This is the source of energy in stars and hydrogen bombs.

graph of binding energy From the graph it can be seen that the greatest release of energy occurs fusing hydrogen to form helium.

graph of binding energy Elements heavier than iron only release energy when split, as was the case with the plutonium and uranium used in the first atomic bombs.

Sources of Heavy Elements Elements heavier than iron are made in stars by capturing neutrons onto atomic nuclei. This takes place in some red giants and in supernovae explosions.

Sources of Heavy Elements A new isotope is created when an atom captures a neutron. If this isotope is unstable then a neutron can convert into a proton, releasing an electron. This is called beta decay and is a form of radioactive decay also observed on Earth. By converting a neutron into a proton the atom has increased its atomic number by one and become the adjacent element in the periodic table. It may then capture another neutron, and so on, so that using iron as seed nuclei it is possible to build all the elements heavier than iron in the periodic table.

Sources of Heavy Elements The difference between element synthesis in red giants and supernovae is that in supernovae the flux of neutrons is greater and it is possible for the atom to capture a second, or third neutron, before it has a chance to beta-decay. This leads to the production of a different set of elements to those produced in red giants, where the flux of neutrons is much less.

graph of binding energy Radioactive decay happens when an unstable nucleus emits radiation. It becomes more stable. The daughter nuclei always have a higher binding energy per nucleon than the parent nucleus

nuclear fission The large nuclei have a lower binding energy per nucleon. They are less stable. This lack of stability is usually shown by radioactive decay, which occurs in a predictable way. Very rarely a large nucleus will split up spontaneously into fragments. Splitting of the nucleus is called fission.

nuclear fission Consider the nucleus as a “wobbly drop”. Nuclei are not tidy and neatly arranged rows of neutrons and protons. They are microscopic bedlam. The strong nuclear force acts between neighboring nucleons

nuclear fission The nucleons are not linked with the same neighbors all the time.  Instead they are constantly swapping about.  However the enough of the nucleons linked to stop the repulsive electromagnetic force tearing the nucleus apart. Now we imagine the nucleus as a wobbly drop:

nuclear fission Now if the nucleus gets to this shape:

nuclear fission The nucleus flies apart in two fragments: The detail of the mechanism that drives this process is complicated and is based on Heisenberg’s uncertainty principle.  A similar model can be used to explain how alpha decay works.

nuclear fission We can induce fission in large nuclei such as uranium-235.  The most common isotope of uranium, U-238, does not split easily, but the 235 isotope does.  We induce fission by “tickling” the nucleus with a “thermal” neutron.  The neutron has to have the right kinetic energy: Too little kinetic energy means that the neutron will bounce off the nucleus; Too much kinetic energy means that the neutron will go right through the nucleus. Just right means that the neutron will be captured by the strong force, which is attractive between nucleons.  The neutron gives the nucleus enough energy to resonate, and this will make the nucleus neck as shown previously

nuclear fission The tickled nucleus flies apart into a number of fragments, leaving on average three neutrons left over. These too are able to tickle other nuclei and make them split. Each neutron spawns three more neutrons in each fission, so we get a chain reaction.

nuclear fission There is a mass defect in the products of the fission so energy is given out. In an uncontrolled chain reaction, the energy is given out in the form of a violent explosion, which is many times more powerful than the explosive decomposition of TNT. In an atomic bomb, the mass that is converted to energy is about 20 grams.

nuclear fusion Light nuclei are joined together Increases the binding energy per nucleon Results in lots of energy being given out An example:

nuclear fusion It is not simply a case of sticking some deuterium and tritium together and shaking it up. Each nucleus has to have sufficient energy to: Overcome electrostatic repulsion from the protons; Overcome the repulsive strong force which is found outside the region of the strong force. This means that the gases have to be heated to a very high temperature, 100 million Kelvin.

nuclear fusion main source of the Sun’s energy

problems involving fission and fusion reactions Data to use: Mass of deuterium nucleus = 3.3425  10-27 kg Mass of tritium nucleus = 6.6425  10-27 kg Mass of helium nucleus = 6.6465 10-27 kg Mass of a neutron = 1.675  10-27 kg What is the energy in J and eV released in this reaction above?

URANIUM, PLUTONIUM, & THE BOMB When uranium ore is extracted from the earth, most of the uranium is removed from the crushed rock during the milling process, but the radioactive decay products are left in the tailings. Thus 85 percent of the radioactivity of the original ore is discarded in the mill tailings.

URANIUM, PLUTONIUM, & THE BOMB Depleted uranium remains radioactive for literally billions of years, and over these long periods of time it will continue to produce all of its radioactive decay products; thus depleted uranium actually becomes more radioactive as the centuries and millennia go by because these decay products accumulate.

URANIUM, PLUTONIUM, & THE BOMB Natural uranium is a blend of two types : U-235 and U-238. At a uranium enrichment plant, the concentration of U-235 is increased by discarding some U-238. The cast-off uranium (mainly U-238), called ''depleted uranium'', has virtually no commercial value.

URANIUM, PLUTONIUM, & THE BOMB There are several important military uses for depleted uranium : when placed in a reactor, it breeds plutonium -- a powerful nuclear explosive; when incorporated into an H-bomb, it doubles the explosive power of the weapon; when used to coat conventional bullets and shells, it makes them armour-piercing; when used as a metallic alloy in tanks and other vehicles, it provides armour-plating.

Breeding plutonium-239 from uranium-238

How To Make an H-Bomb Howard Morland wrote a magazine article explaining how an "H-Bomb" -- or "thermonuclear bomb" -- is made, using only publicly available information. In the photo, he is standing on the steps of the US Supreme Court holding a cut-away model of the H-bomb.

How To Make an H-Bomb An H-bomb is a three-stage weapon: fission, fusion, and then fission again. The first stage, called the "trigger" (the black ball at the top), is a small plutonium bomb similar to the one dropped on Nagasaki in 1945. The energy release at this stage is mainly due to nuclear fission -- because the atoms of plutonium are split.

How To Make an H-Bomb Tritium is often added to the centre of the plutonium core to "boost" the fission explosion with some additional fusion energy. Boosted or not, however, the only importance of this first-stage explosion is to irradiate and heat the material in the central column to 100 million degrees celsius so that a much more powerful fusion reaction can be started there.

How To Make an H-Bomb The second stage explosion is due to nuclear fusion in the central column. The main fusion reaction involves concentrated deuterium and tritium (both heavy isotopes of hydrogen) -- which become spontaneously available when neutrons from the first stage explosion bombard a solid material called "lithium deuteride" located in the central column. When this hydrogen-rich mix is heated to 100 million degrees, the deuterium and tritium atoms "fuse" together, releasing enormous amounts of energy. This is the "H" or "thermonuclear" part of the bomb.

How To Make an H-Bomb Then comes the third stage. The fusion reaction gives off an incredible burst of extremely powerful neutrons -- so powerful that they can split or "fission" atoms of uranium-238 (called "depleted uranium") -- which is impossible at lower energy levels. This third stage more than doubles the power of the explosion, and produces most of the radioactive fallout from the weapon.

How To Make an H-Bomb Unlike fission bombs, which rely only on nuclear fission, and which can achieve explosions equivalent to thousands of tons of TNT ("kilotons"), the power of an H-bomb or thermonuclear weapon has no practical limit -- it can be made as powerful as you want, by adding more deuterium/tritium to the second stage. Most H-bombs are measured in "megatons" (equivalent to the explosive power of MILLIONS of tons of TNT -- hundreds of times, or even a thousand times more powerful than a fission bomb).