Radiometric dating decay curves
The atomic nucleus which is in the center of the atom is buffered by surrounding electrons and external conditions.
Because of this, the study of decay is independent of the element's environment.
A proton from Beryllium-7 captures a single electron and becomes a neutron.
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).In such cases, it is possible that the half-life of the parent nuclei is longer or shorter than the half-life of the daughter nuclei.Depending upon the substance, it is possible that both parent and daughter nuclei have similar half lives.In other words, the decay rate is independent of an element's physical state such as surrounding temperature and pressure.For a given element, the decay or disintegration rate is proportional to the number of atoms and the activity measured in terms of atoms per unit time.
Carbon 14 (C-14) is produced in the upper atmosphere through the collision of cosmic rays with atmospheric 14N.