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In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a decay chain as a function of time, based on the decay rates and initial abundances. The model was formulated by Ernest Rutherford in 1905 [1] and the analytical solution was provided by Harry Bateman in 1910. [2]
Computing the total disintegration energy given by the equation = (), where m i is the initial mass of the nucleus, m f is the mass of the nucleus after particle emission, and m p is the mass of the emitted (alpha-)particle, one finds that in certain cases it is positive and so alpha particle emission is possible, whereas other decay modes ...
Defining equation SI units Dimension Number of atoms N = Number of atoms remaining at time t. N 0 = Initial number of atoms at time t = 0 N D = Number of atoms decayed at time t = + dimensionless dimensionless Decay rate, activity of a radioisotope: A = Bq = Hz = s −1 [T] −1: Decay constant: λ
Heavy nuclides are susceptible to α decay, and these nuclear reactions have the generic form, A Z X → A-4 Z-2 X′ + 4 2 He. As in β decay, the decay product X′ has greater binding energy and it is closer to the middle of the valley of stability. The α particle carries away two neutrons and two protons, leaving a lighter nuclide. Since ...
Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha, beta, and gamma decay.
Nuclear reactions may be shown in a form similar to chemical equations, for which invariant mass must balance for each side of the equation, and in which transformations of particles must follow certain conservation laws, such as conservation of charge and baryon number (total atomic mass number). An example of this notation follows:
Nuclear chemistry is the sub-field of chemistry dealing with radioactivity, nuclear processes, and transformations in the nuclei of atoms, such as nuclear transmutation and nuclear properties. It is the chemistry of radioactive elements such as the actinides , radium and radon together with the chemistry associated with equipment (such as ...
In contrast to beta decay, the fundamental interactions responsible for alpha decay are a balance between the electromagnetic force and nuclear force. Alpha decay results from the Coulomb repulsion [4] between the alpha particle and the rest of the nucleus, which both have a positive electric charge, but which is kept in check by the nuclear force.