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11.9: Nuclear Fission and Nuclear Fusion

  • Page ID
    86620
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    Learning Objectives
    • Explain nuclear fission and fusion processes.
    • Write and balance nuclear fission and fusion equations.
    • Relate the concepts of critical mass and nuclear chain reactions.

    Nuclear fusion and nuclear fission are two different types of energy-releasing reactions in which energy is released from high-powered atomic bonds between the particles within the nucleus. The main difference between these two processes is that fission is the splitting of an atom into two or more smaller ones while fusion is the fusing of two or more smaller atoms into a larger one.

    Protons and neutrons make up a nucleus, which is the foundation of nuclear science. Fission and fusion involves the dispersal and combination of elemental nucleus and isotopes, and part of nuclear science is to understand the process behind this phenomenon. Adding up the individual masses of each of these subatomic particles of any given element will always give you a greater mass than the mass of the nucleus as a whole. The missing idea in this observation is the concept called nuclear binding energy. Nuclear binding energy is the energy required to keep the protons and neutrons of a nucleus intact, and the energy that is released during a nuclear fission or fusion is nuclear power. There are some things to consider however. The mass of an element's nucleus as a whole is less than the total mass of its individual protons and neutrons.

    To calculate the energy released during mass destruction in both nuclear fission and fusion, we use Einstein’s equation that equates energy and mass:

    \[ E=mc^2 \label{1} \]

    with \(m\) is mass (kilograms), \(c\) is speed of light (meters/sec) and \(E\) is energy (Joules).

    Nuclear Fission

    Many heavier elements with smaller binding energies per nucleon can decompose into more stable elements that have intermediate mass numbers and larger binding energies per nucleon—that is, mass numbers and binding energies per nucleon that are closer to the “peak” of the binding energy graph near 56. Sometimes neutrons are also produced. This decomposition is called fission, the breaking of a large nucleus into smaller pieces. The breaking is rather random with the formation of a large number of different products. Fission usually does not occur naturally, but is induced by bombardment with neutrons. The first reported nuclear fission occurred in 1939 when three German scientists, Lise Meitner, Otto Hahn, and Fritz Strassman, bombarded uranium-235 atoms with slow-moving neutrons that split the U-238 nuclei into smaller fragments that consisted of several neutrons and elements near the middle of the periodic table. Since then, fission has been observed in many other isotopes, including most actinide isotopes that have an odd number of neutrons. A typical nuclear fission reaction is shown in Figure \(\PageIndex{1}\).

    A diagram is shown which has a white sphere labeled “superscript, 1, subscript 0, n” followed by a right-facing arrow and a large sphere composed of many smaller white and green spheres labeled “superscript, 235, subscript 92, U.” The single sphere has impacted the larger sphere. A right-facing arrow leads from the larger sphere to a vertical dumbbell shaped collection of the same white and green spheres labeled “superscript, 236, subscript 92, U, Unstable nucleus.” Two right-facing arrows lead from the top and bottom of this structure to two new spheres that are also composed of green and white spheres and are slightly smaller than the others. The top sphere is labeled “superscript, 92, subscript 36, K r” while the lower one is labeled “superscript, 141, subscript 56, B a.” A starburst pattern labeled “Energy” lies between these two spheres and has three right-facing arrows leading from it to three white spheres labeled “3, superscript, 1, subscript 0, n.” A balanced nuclear equation is written below the diagram and says “superscript, 235, subscript 92, U, plus sign, superscript, 1, subscript 0, n, yield arrow, superscript, 236, subscript 92, U, yield arrow, superscript, 141, subscript 56, B a, plus sign, superscript, 92, subscript 36, K r, plus sign, 3, superscript, 1, subscript 0, n.”
    Figure \(\PageIndex{1}\): When a slow neutron hits a fissionable U-235 nucleus, it is absorbed and forms an unstable U-236 nucleus. The U-236 nucleus then rapidly breaks apart into two smaller nuclei (in this case, Ba-141 and Kr-92) along with several neutrons (usually two or three), and releases a very large amount of energy.

    Among the products of Meitner, Hahn, and Strassman’s fission reaction were barium, krypton, lanthanum, and cerium, all of which have nuclei that are more stable than uranium-235. Since then, hundreds of different isotopes have been observed among the products of fissionable substances. A few of the many reactions that occur for U-235, and a graph showing the distribution of its fission products and their yields, are shown in Figure \(\PageIndex{2}\). Similar fission reactions have been observed with other uranium isotopes, as well as with a variety of other isotopes such as those of plutonium.

    Five nuclear equations and a graph are shown. The first equation is “superscript, 235, subscript 92, U, plus sign, superscript, 1, subscript 0, n, yield arrow, superscript, 236, subscript 92, U, yield arrow, superscript, 90, subscript 38, S r, plus sign, superscript, 144, subscript 54, X e, plus sign, 2, superscript, 1, subscript 0, n.” The second equation is “superscript, 235, subscript 92, U, plus sign, superscript, 1, subscript 0, n, yield arrow, superscript, 236, subscript 92, U, yield arrow, superscript, 87, subscript 35, B r, plus sign, superscript, 146, subscript 57, L a, plus sign, 3, superscript, 1, subscript 0, n.” The third equation is “superscript, 235, subscript 92, U, plus sign, superscript, 1, subscript 0, n, yield arrow, superscript, 236, subscript 92, U, yield arrow, superscript, 97, subscript 37, R b, plus sign, superscript, 137, subscript 55, C s, plus sign, 3, superscript, 1, subscript 0, n.” The fourth equation is “superscript, 235, subscript 92, U, plus sign, superscript, 1, subscript 0, n, yield arrow, superscript, 236, subscript 92, U, yield arrow, superscript, 137, subscript 52, T e, plus sign, superscript, 97, subscript 40, Z r, plus sign, 2, superscript, 1, subscript 0, n.” The fifth equation is “superscript, 235, subscript 92, U, plus sign, superscript, 1, subscript 0, n, yield arrow, superscript, 236, subscript 92, U, yield arrow, superscript, 141, subscript 56, B a, plus sign, superscript, 92, subscript 36, K r, plus sign, 3, superscript, 1, subscript 0, n.” A graph is also shown where the y-axis is labeled “Fission yield, open parenthesis, percent sign, close parenthesis” and has values of 0 to 9 in increments of 1 while the x-axis is labeled “Mass number” and has values of 60 to 180 in increments of 20. The graph begins near point “65, 0” and rises rapidly to near “92, 6.6,” then drops just as rapidly to “107, 0” and remains there to point “127, 0.” The graph then rises again to near “132, 8,” then goes up and down a bit before falling to a point “153, 0,” and going horizontal.
    Figure \(\PageIndex{2}\): (a) Nuclear fission of U-235 produces a range of fission products. (b) The larger fission products of U-235 are typically one isotope with a mass number around 85–105, and another isotope with a mass number that is about 50% larger, that is, about 130–150.

    A tremendous amount of energy is produced by the fission of heavy elements. For instance, when one mole of U-235 undergoes fission, the products weigh about 0.2 grams less than the reactants; this “lost” mass is converted into a very large amount of energy, about 1.8 × 1010 kJ per mole of U-235. Nuclear fission reactions produce incredibly large amounts of energy compared to chemical reactions. The fission of 1 kilogram of uranium-235, for example, produces about 2.5 million times as much energy as is produced by burning 1 kilogram of coal.

    When undergoing fission U-235 produces two “medium-sized” nuclei, and two or three neutrons. These neutrons may then cause the fission of other uranium-235 atoms, which in turn provide more neutrons that can cause fission of even more nuclei, and so on. If this occurs, we have a nuclear chain reaction (Figure \(\PageIndex{3}\)). On the other hand, if too many neutrons escape the bulk material without interacting with a nucleus, then no chain reaction will occur.

    A diagram is shown which has a white sphere labeled “superscript, 1, subscript 0, n” followed by a right-facing arrow and a large sphere composed of many smaller white and green spheres labeled “superscript, 235, subscript 92, U.” The single sphere has impacted the larger sphere. A right-facing arrow leads from the larger sphere to a pair of smaller spheres which are collections of the same white and green spheres. The upper of these two images is labeled “superscript, 93, subscript 36, K r” while the lower of the two is labeled “superscript, 142, subscript 56, B a.” A starburst pattern labeled “Energy” lies between these two spheres and has three right-facing arrows leading from it to three white spheres labeled “ superscript, 1, subscript 0, n.”  An equation below this portion of the diagram reads ““superscript, 235, subscript 92, U, plus sign, superscript, 1, subscript 0, n, yield arrow, superscript, 140, subscript 56, B a, plus sign, superscript 90, subscript 36, K r, plus sign, 3, superscript 1, subscript 0, n.”  A right-facing arrow leads from each of these white spheres to three larger spheres, each composed of many smaller green and white spheres and labeled, from top to bottom as “a, superscript,235, subscript 92, U,” “b, superscript,235, subscript 92, U” and “c, superscript,235, subscript 92, U.” Each of these spheres is followed by a right-facing arrow which points to a pair of smaller spheres composed of the same green and white spheres with starburst patterns in between each pair labeled “Energy.” The spheres of the top pair are labeled, from top to bottom, “superscript, 96, subscript 37, R b” and “superscript, 137, subscript 55, C s.” The spheres of the middle pair are labeled, from top to bottom, “superscript, 90, subscript 38, S r” and “superscript, 144, subscript 54, X e.” The spheres of the bottom pair are labeled, from top to bottom, “superscript, 87, subscript 35, B r” and “superscript, 146, subscript 57, L a.” Each pair of spheres is followed by three right-facing arrows leading to three white spheres labeled “superscript, 1, subscript 0, n.”  Below the diagram are three nuclear equations. Equation a reads “superscript, 235, subscript 92, U, plus sign, superscript, 1, subscript 0, n, yield arrow, superscript, 96, subscript 37, R b, plus sign, superscript 137, subscript 55, C s, plus sign, 3, superscript 1, subscript 0, n.” Equation b reads “superscript, 235, subscript 92, U, plus sign, superscript, 1, subscript 0, n, yield arrow, superscript, 90, subscript 38, S r, plus sign, superscript144, subscript 54, X e, plus sign, 2, superscript 1, subscript 0, n.” Equation c reads “superscript, 235, subscript 92, U, plus sign, superscript, 1, subscript 0, n, yield arrow, superscript, 87, subscript 35, B r, plus sign, superscript 146, subscript 57, L a, plus sign, 3, superscript 1, subscript 0, n”
    Figure \(\PageIndex{3}\): The fission of a large nucleus, such as U-235, produces two or three neutrons, each of which is capable of causing fission of another nucleus by the reactions shown. If this process continues, a nuclear chain reaction occurs.

    Material that can sustain a nuclear fission chain reaction is said to be fissile or fissionable. (Technically, fissile material can undergo fission with neutrons of any energy, whereas fissionable material requires high-energy neutrons.) Nuclear fission becomes self-sustaining when the number of neutrons produced by fission equals or exceeds the number of neutrons absorbed by splitting nuclei plus the number that escape into the surroundings. The amount of a fissionable material that will support a self-sustaining chain reaction is a critical mass. An amount of fissionable material that cannot sustain a chain reaction is a subcritical mass. An amount of material in which there is an increasing rate of fission is known as a supercritical mass.

    Nuclear power plants are designed in such a way that they cannot form a supercritical mass of fissionable material and therefore cannot create a nuclear explosion. But as history has shown, failures of systems and safeguards can cause catastrophic accidents, including chemical explosions and nuclear meltdowns (damage to the reactor core from overheating). The following Chemistry in Everyday Life feature explores three infamous meltdown incidents.

    Nuclear Accidents

    The importance of cooling and containment are amply illustrated by three major accidents that occurred with the nuclear reactors at nuclear power generating stations in the United States (Three Mile Island), the former Soviet Union (Chernobyl), and Japan (Fukushima).

    In March 1979, the cooling system of the Unit 2 reactor at Three Mile Island Nuclear Generating Station in Pennsylvania failed, and the cooling water spilled from the reactor onto the floor of the containment building. After the pumps stopped, the reactors overheated due to the high radioactive decay heat produced in the first few days after the nuclear reactor shut down. The temperature of the core climbed to at least 2200 °C, and the upper portion of the core began to melt. In addition, the zirconium alloy cladding of the fuel rods began to react with steam and produced hydrogen:

    \[\ce{Zr}(s)+\ce{2H2O}(g)⟶\ce{ZrO2}(s)+\ce{2H2}(g) \nonumber \]

    The hydrogen accumulated in the confinement building, and it was feared that there was danger of an explosion of the mixture of hydrogen and air in the building. Consequently, hydrogen gas and radioactive gases (primarily krypton and xenon) were vented from the building. Within a week, cooling water circulation was restored and the core began to cool. The plant was closed for nearly 10 years during the cleanup process.

    Although zero discharge of radioactive material is desirable, the discharge of radioactive krypton and xenon, such as occurred at the Three Mile Island plant, is among the most tolerable. These gases readily disperse in the atmosphere and thus do not produce highly radioactive areas. Moreover, they are noble gases and are not incorporated into plant and animal matter in the food chain. Effectively none of the heavy elements of the core of the reactor were released into the environment, and no cleanup of the area outside of the containment building was necessary (Figure \(\PageIndex{4}\)).

    Two photos, labeled “a” and “b” are shown. Photo a is an aerial view of a nuclear power plant. Photo b shows a small group of men walking through a room filled with electronics.
    Figure \(\PageIndex{4}\): (a) In this 2010 photo of Three Mile Island, the remaining structures from the damaged Unit 2 reactor are seen on the left, whereas the separate Unit 1 reactor, unaffected by the accident, continues generating power to this day (right). (b) President Jimmy Carter visited the Unit 2 control room a few days after the accident in 1979.

    Another major nuclear accident involving a reactor occurred in April 1986, at the Chernobyl Nuclear Power Plant in Ukraine, which was still a part of the former Soviet Union. While operating at low power during an unauthorized experiment with some of its safety devices shut off, one of the reactors at the plant became unstable. Its chain reaction became uncontrollable and increased to a level far beyond what the reactor was designed for. The steam pressure in the reactor rose to between 100 and 500 times the full power pressure and ruptured the reactor. Because the reactor was not enclosed in a containment building, a large amount of radioactive material spewed out, and additional fission products were released, as the graphite (carbon) moderator of the core ignited and burned. The fire was controlled, but over 200 plant workers and firefighters developed acute radiation sickness and at least 32 soon died from the effects of the radiation. It is predicted that about 4000 more deaths will occur among emergency workers and former Chernobyl residents from radiation-induced cancer and leukemia. The reactor has since been encapsulated in steel and concrete, a now-decaying structure known as the sarcophagus. Almost 30 years later, significant radiation problems still persist in the area, and Chernobyl largely remains a wasteland.

    In 2011, the Fukushima Daiichi Nuclear Power Plant in Japan was badly damaged by a 9.0-magnitude earthquake and resulting tsunami. Three reactors up and running at the time were shut down automatically, and emergency generators came online to power electronics and coolant systems. However, the tsunami quickly flooded the emergency generators and cut power to the pumps that circulated coolant water through the reactors. High-temperature steam in the reactors reacted with zirconium alloy to produce hydrogen gas. The gas escaped into the containment building, and the mixture of hydrogen and air exploded. Radioactive material was released from the containment vessels as the result of deliberate venting to reduce the hydrogen pressure, deliberate discharge of coolant water into the sea, and accidental or uncontrolled events.

    An evacuation zone around the damaged plant extended over 12.4 miles away, and an estimated 200,000 people were evacuated from the area. All 48 of Japan’s nuclear power plants were subsequently shut down, remaining shuttered as of December 2014. Since the disaster, public opinion has shifted from largely favoring to largely opposing increasing the use of nuclear power plants, and a restart of Japan’s atomic energy program is still stalled (Figure \(\PageIndex{5}\)).

    A photo and a map, labeled “a” and “b,” respectively, are shown. Photo a shows a man in a body-covering safety suit working near a series of blue, plastic coated containers. Map b shows a section of land with the ocean on each side. Near the upper right side of the land is a small red dot, labeled “greater than, 12.5, m R backslash, h r,” that is surrounded by a zone of orange that extends in the upper left direction labeled “2.17, dash, 12.5, m R backslash, h r.” The orange is surrounded by an outline of yellow labeled “1.19, dash, 2.17, m R backslash, h r” and a wider outline of green labeled “0.25, dash, 1.19, m R backslash, h r.” A large area of light blue, labeled “0.03, dash, 0.25, m R backslash, h r” surrounds the green area and extends to the lower middle of the map. A large section of the lower middle and left of the land is covered by dark blue, labeled “less than 0.03, m R backslash, h r.”
    Figure \(\PageIndex{5}\): (a) After the accident, contaminated waste had to be removed, and (b) an evacuation zone was set up around the plant in areas that received heavy doses of radioactive fallout. (credit a: modification of work by “Live Action Hero”/Flickr)

    The energy produced by a reactor fueled with enriched uranium results from the fission of uranium as well as from the fission of plutonium produced as the reactor operates. As discussed previously, the plutonium forms from the combination of neutrons and the uranium in the fuel. In any nuclear reactor, only about 0.1% of the mass of the fuel is converted into energy. The other 99.9% remains in the fuel rods as fission products and unused fuel. All of the fission products absorb neutrons, and after a period of several months to a few years, depending on the reactor, the fission products must be removed by changing the fuel rods. Otherwise, the concentration of these fission products would increase and absorb more neutrons until the reactor could no longer operate.

    Spent fuel rods contain a variety of products, consisting of unstable nuclei ranging in atomic number from 25 to 60, some transuranium elements, including plutonium and americium, and unreacted uranium isotopes. The unstable nuclei and the transuranium isotopes give the spent fuel a dangerously high level of radioactivity. The long-lived isotopes require thousands of years to decay to a safe level. The ultimate fate of the nuclear reactor as a significant source of energy in the United States probably rests on whether or not a politically and scientifically satisfactory technique for processing and storing the components of spent fuel rods can be developed.

    Nuclear Fusion

    The process of converting very light nuclei into heavier nuclei is also accompanied by the conversion of mass into large amounts of energy, a process called fusion. The principal source of energy in the sun is a net fusion reaction in which four hydrogen nuclei fuse and produce one helium nucleus and two positrons. This is a net reaction of a more complicated series of events:

    \[\ce{4^1_1H ⟶ ^4_2He + 2^0_{+1}}\]

    A helium nucleus has a mass that is 0.7% less than that of four hydrogen nuclei; this lost mass is converted into energy during the fusion. This reaction produces about 3.6 × 1011 kJ of energy per mole of \(\ce{^4_2He}\) produced. This is somewhat larger than the energy produced by the nuclear fission of one mole of U-235 (1.8 × 1010 kJ), and over 3 million times larger than the energy produced by the (chemical) combustion of one mole of octane (5471 kJ).

    It has been determined that the nuclei of the heavy isotopes of hydrogen, a deuteron, \(^2_1\) and a triton, \(^3_1\), undergo fusion at extremely high temperatures (thermonuclear fusion). They form a helium nucleus and a neutron:

    \[\ce{^2_1H + ^3_1H ⟶ ^4_2He + 2^1_0n}\]

    This change proceeds with a mass loss of 0.0188 amu, corresponding to the release of 1.69 × 109 kilojoules per mole of \(\ce{^4_2He}\) formed. The very high temperature is necessary to give the nuclei enough kinetic energy to overcome the very strong repulsive forces resulting from the positive charges on their nuclei so they can collide.

    330px-Deuterium-tritium_fusion.svg.png
    Figure \(\PageIndex{6}\): Fusion of deuterium with tritium creating helium-4, freeing a neutron, and releasing 17.59 MeV of energy, as an appropriate amount of mass changing forms to appear as the kinetic energy of the products, in agreement with kinetic \(E = Δmc^2\), where Δm is the change in rest mass of particles.[Image use with permission via Wikipedia (Wykis)

    The most important fusion process in nature is the one that powers stars. In the 20th century, it was realized that the energy released from nuclear fusion reactions accounted for the longevity of the Sun and other stars as a source of heat and light. The fusion of nuclei in a star, starting from its initial hydrogen and helium abundance, provides that energy and synthesizes new nuclei as a byproduct of that fusion process. The prime energy producer in the Sun is the fusion of hydrogen to form helium, which occurs at a solar-core temperature of 14 million kelvin. The net result is the fusion of four protons into one alpha particle, with the release of two positrons, two neutrinos (which changes two of the protons into neutrons), and energy (Figure \(\PageIndex{7}\)).

    800px-The_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA's_Solar_Dynamics_Observatory_-_20100819.jpg
    678px-FusionintheSun.svg.png
    Figure \(\PageIndex{7}\): (left) The Sun is a main-sequence star, and thus generates its energy by nuclear fusion of hydrogen nuclei into helium. In its core, the Sun fuses 620 million metric tons of hydrogen each second. (right) The proton-proton chain dominates in stars the size of the Sun or smaller.
    Example \(\PageIndex{1}\)

    Calculate the energy released in each of the following hypothetical processes.

    1. \(\ce{3 ^4_2He \rightarrow ^{12}_6C}\)
    2. \(\ce{6 ^1_1H + 6 ^1_0n \rightarrow ^{12}_6C}\)
    3. \(\ce{6 ^2_1D \rightarrow ^{12}_6C}\)
    Solution
    1. \(Q_a = 3 \times 4.0026 - 12.000) \,amu \times (1.4924\times 10^{-10} \,J/amu) = 1.17 \times 10^{-12} \,J\)
    2. \(Q_b = (6 \times (1.007825 + 1.008665) - 12.00000)\, amu \times (1.4924\times 10^{1-0} J/amu) = 1.476\times 10^{-11} \,J\)
    3. \(Q_c = 6 \times 2.014102 - 12.00000 \, amu \times (1.4924\times 10^{-10} \, J/amu) = 1.263\times 10^{-11}\, J\)

    Fusion of \(\ce{He}\) to give \(\ce{C}\) releases the least amount of energy, because the fusion to produce He has released a large amount. The difference between the second and the third is the binding energy of deuterium. The conservation of mass-and-energy is well illustrated in these calculations. On the other hand, the calculation is based on the conservation of mass-and-energy.

    Nuclear Reactors

    Useful fusion reactions require very high temperatures for their initiation—about 15,000,000 K or more. At these temperatures, all molecules dissociate into atoms, and the atoms ionize, forming plasma. These conditions occur in an extremely large number of locations throughout the universe—stars are powered by fusion. Humans have already figured out how to create temperatures high enough to achieve fusion on a large scale in thermonuclear weapons. A thermonuclear weapon such as a hydrogen bomb contains a nuclear fission bomb that, when exploded, gives off enough energy to produce the extremely high temperatures necessary for fusion to occur.

    Two photos are shown and labeled “a” and “b.” Photo a shows a model of the ITER reactor made up of colorful components. Photo b shows a close-up view of the end of a long, mechanical arm made up of many metal components.
    Figure \(\PageIndex{8}\): (a) This model is of the International Thermonuclear Experimental Reactor (ITER) reactor. Currently under construction in the south of France with an expected completion date of 2027, the ITER will be the world’s largest experimental Tokamak nuclear fusion reactor with a goal of achieving larg\times 10^{scale sustained energy production. (b) In 2012, the National Ignition Facility at Lawrence Livermore National Laboratory briefly produced over 500,000,000,000 watts (500 terawatts, or 500 TW) of peak power and delivered 1,850,000 joules (1.85 MJ) of energy, the largest laser energy ever produced and 1000 times the power usage of the entire United States in any given moment. Although lasting only a few billionths of a second, the 192 lasers attained the conditions needed for nuclear fusion ignition. This image shows the target prior to the laser shot. (credit a: modification of work by Stephan Mosel)

    Another much more beneficial way to create fusion reactions is in a fusion reactor, a nuclear reactor in which fusion reactions of light nuclei are controlled. Because no solid materials are stable at such high temperatures, mechanical devices cannot contain the plasma in which fusion reactions occur. Two techniques to contain plasma at the density and temperature necessary for a fusion reaction are currently the focus of intensive research efforts: containment by a magnetic field and by the use of focused laser beams (Figure \(\PageIndex{8}\)). A number of large projects are working to attain one of the biggest goals in science: getting hydrogen fuel to ignite and produce more energy than the amount supplied to achieve the extremely high temperatures and pressures that are required for fusion. At the time of this writing, there are no self-sustaining fusion reactors operating in the world, although small-scale controlled fusion reactions have been run for very brief periods.

    Contributors and Attributions


    11.9: Nuclear Fission and Nuclear Fusion is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by LibreTexts.

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