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A Identify the reactants and the products from the information given. B Use the values of A and Z to identify any missing components needed to balance the equation. The reaction is as follows:. The balanced nuclear equation is thus.
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A As in part a , we are given the identities of the reactant and one of the products—in this case, a positron. The unbalanced nuclear equation is therefore. The balanced nuclear equation for the reaction is as follows:. Predict the kind of nuclear change each unstable nuclide undergoes when it decays. Based on the neutron-to-proton ratio and the value of Z , predict the type of nuclear decay reaction that will produce a more stable nuclide. The nuclei of all elements with atomic numbers greater than 83 are unstable. Thus all isotopes of all elements beyond bismuth in the periodic table are radioactive.
This series of sequential alpha- and beta-decay reactions is called a radioactive decay series. A fourth series, the decay of neptunium to bismuth in 11 steps, is known to have occurred on the primitive Earth. Due to these radioactive decay series, small amounts of very unstable isotopes are found in ores that contain uranium or thorium. These rare, unstable isotopes should have decayed long ago to stable nuclei with a lower atomic number, and they would no longer be found on Earth. Because they are generated continuously by the decay of uranium or thorium, however, their amounts have reached a steady state, in which their rate of formation is equal to their rate of decay.
In some cases, the abundance of the daughter isotopes can be used to date a material or identify its origin. The discovery of radioactivity in the late 19th century showed that some nuclei spontaneously transform into nuclei with a different number of protons, thereby producing a different element. When scientists realized that these naturally occurring radioactive isotopes decayed by emitting subatomic particles, they realized that—in principle—it should be possible to carry out the reverse reaction, converting a stable nucleus to another more massive nucleus by bombarding it with subatomic particles in a nuclear transmutation reaction.
As shown in the following equation, a proton is emitted in the process:. Very light targets such as Li, Be, and B reacted differently, however, emitting a new kind of highly penetrating radiation rather than a proton. Because neither a magnetic field nor an electrical field could deflect these high-energy particles, Rutherford concluded that they were electrically neutral.
Other observations suggested that the mass of the neutral particle was similar to the mass of the proton. The reaction that Chadwick initially used to explain the production of neutrons was as follows:. Neutrons have no electrical charge, however, so they are not repelled by the nucleus. Hence bombardment with neutrons is a much easier way to prepare new isotopes of the lighter elements.
In fact, carbon is formed naturally in the atmosphere by bombarding nitrogen with neutrons generated by cosmic rays:. For each 27 Al that reacted, one neutron was released. Identify the product nuclide and write a balanced nuclear equation for this transmutation reaction. Given: reactants in a nuclear transmutation reaction. Asked for: product nuclide and balanced nuclear equation. A Based on the reactants and one product, identify the other product of the reaction.
Use conservation of mass and charge to determine the values of Z and A of the product nuclide and thus its identity. B Write the balanced nuclear equation for the reaction. With one neutron released, conservation of mass requires that the mass number of the other product be 3 greater than the mass number of the target. In this case, the mass number of the target is 27, so the mass number of the product will be B The balanced nuclear equation for the reaction is as follows:.
Few-Body Problems in Particle, Nuclear, Atomic, and Molecular Physics
Because all isotopes of technetium are radioactive and have short half-lives, it does not exist in nature. Technetium can, however, be prepared by nuclear transmutation reactions. Identify the other product of the reaction and write a balanced nuclear equation for this transmutation reaction. Any isotope that can undergo a nuclear fission reaction when bombarded with neutrons is called a fissile isotope.
Moreover, every fission event of a given nuclide does not give the same products; more than 50 different fission modes have been identified for uranium, for example. Consequently, nuclear fission of a fissile nuclide can never be described by a single equation. As shown in Equation Initially, a neutron combines with a U nucleus to form U, which is unstable and undergoes beta decay to produce Np:.
A device called a particle accelerator is used to accelerate positively charged particles to the speeds needed to overcome the electrostatic repulsions between them and the target nuclei by using electrical and magnetic fields. Rapid alternation of the polarity of the electrodes along the tube causes the particles to be alternately accelerated toward a region of opposite charge and repelled by a region with the same charge, resulting in a tremendous acceleration as the particle travels down the tube.
To achieve the same outcome in less space, a particle accelerator called a cyclotron forces the charged particles to travel in a circular path rather than a linear one. The particles are injected into the center of a ring and accelerated by rapidly alternating the polarity of two large D-shaped electrodes above and below the ring, which accelerates the particles outward along a spiral path toward the target. The length of a linear accelerator and the size of the D-shaped electrodes in a cyclotron severely limit the kinetic energy that particles can attain in these devices.
These limitations can be overcome by using a synchrotron, a hybrid of the two designs. A synchrotron contains an evacuated tube similar to that of a linear accelerator, but the tube is circular and can be more than a mile in diameter. Charged particles are accelerated around the circle by a series of magnets whose polarities rapidly alternate. In nuclear decay reactions or radioactive decay , the parent nucleus is converted to a more stable daughter nucleus.
Nuclei with too many neutrons decay by converting a neutron to a proton, whereas nuclei with too few neutrons decay by converting a proton to a neutron. When an unstable nuclide undergoes radioactive decay, the total number of nucleons is conserved, as is the total positive charge. Six different kinds of nuclear decay reactions are known. Beta decay converts a neutron to a proton and emits a high-energy electron, producing a daughter nucleus with the same mass number as the parent and an atomic number that is higher by 1.
Related Few Particle Problems. in the Nuclear Interaction
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