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Mathematically speaking, the relationship between quantity and time for radioactive decay can be expressed in following way: \[\dfrac = - \lambda N \tag\] or more specifically \[\dfrac = - \lambda N \tag\] or via rearranging the separable differential equation \[\dfrac = - \lambda dt \tag\] by Integrating the equation \[\ln N(t) = - \lambda t C \tag\] with There are two ways to characterize the decay constant: mean-life and half-life. As indicated by the name, mean-life is the average of an element's lifetime and can be shown in terms of following expression \[ N_t=N_o e^ \tag \] \[1 = \int^_ 0 c \cdot N_0 e^ dt = c \cdot \dfrac \tag\] Rearranging the equation: \[ c= \dfrac\] Half-life is the time period that is characterized by the time it takes for half of the substance to decay (both radioactive and non-radioactive elements).
Also, radioactive decay is an exponential decay function which means the larger the quantity of atoms, the more rapidly the element will decay.This element gains stability by passing through various types of decays (19 steps-- also known as the Uranium series) and is converted into Pb-206 (atomic number 82).For further information about different types of decay that Uranium goes through, refer to Decay Pathways).Because of this, the study of decay is independent of the element's environment.In other words, the decay rate is independent of an element's physical state such as surrounding temperature and pressure.
This lighter isotope decays into Lithium-7 through electron capture.