Three assumptions of radiometric dating
If you had an ensemble of identical particles, the probability of finding a given one of them still as they were - with no decay - after some time is given by the mathematical expression This governs what is known as the "decay rate." The rate is unique to different particles and so to different atomic elements.
"Atomic decays" are due to proton or neutron decays: either weakly, incrementing up or down the table of elements; or strongly, often splitting into smaller elements, one of which is often helium.
Most are determined experimentally by institutions such as CERN with the Large Hadron Collider.
Decays are very random, but for different elements are observed to conform to statistically averaged different lifetimes.
For example, a neutron-deficient nucleus may decay weakly by converting a proton in a neutron (to conserve its positive electric charge, it ejects a positron, as well as a neutrino to conserve the quantum lepton number); thus the hypothetical atom loses a proton and increments down the table by one element.
A complex set of rules describes the details of particle decays: historically, the finding of which as been a major objective of particle physics.