Abstract
To develop equations to calculate the half-life of lead isotopes theoretically and compare them with practical results by assuming a simple mathematical model based on the probability of forming alpha particles inside the parent nucleus before tunneling decay them. It is assumed that the presence of an alpha particle inside the nucleus has a Coulomb effect dependent on the reduced mass of the alpha particle with the core, reducing the rest of the effects on the effective potential. The effective radius depends on the mass number of the core and the cluster. The model assumes that there is a number of collisions before tunneling decay, taking into account the existence of the potential barrier penetration coefficient, which expresses the potential permeability of the potential barrier to the alpha particles within it. The model assumes that the Gamow coefficient is dependent on the atomic numbers of both core and cluster, the reduced mass, and the effect of the energy of the alpha particles and takes into account the value of the Coulomb effect.
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