Why do radioactive atoms in a sample decay at different times?

Radioactive atoms in a sample decay at different times because radioactive decay is a spontaneous, individual process governed by probability rather than a simultaneous event for all atoms in a collection.12

While it is impossible to predict exactly when any single, specific atom will decay, the process is statistically predictable for a large number of atoms. Each unstable isotope has an intrinsic property known as a decay constant, which determines the probability of an individual nucleus decaying within a given time interval.23

This behavior is often compared to a population; just as an insurance company cannot predict which specific individual will die but can accurately predict the overall death rate of a large group, scientists can determine the half-life of a radioactive sample. The half-life is the time required for half of the radioactive nuclei in a sample to decay. Because this decay is a random, individual occurrence, the atoms in a sample do not all disappear at once; instead, they decay individually over time, similar to popcorn kernels popping in a pan.3412