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The 235U–207Pb cascade has a half-life of 704 million years and the 238U–206Pb cascade is considerably slower, with a half-life of 4.47 billion years.
So when a mineral grain forms (specifically, when it first cools below its trapping temperature), it effectively sets the uranium-lead "clock" to zero.
Uranium comes in two common isotopes with atomic weights of 235 and 238 (we'll call them 235U and 238U).
Both are unstable and radioactive, shedding nuclear particles in a cascade that doesn't stop until they become lead (Pb).
Because of the high local temperature, however, the reaction time of the radiation-produced intermediates is also very small.
In an intermediate substrate ( second, a time that compares favourably with the duration of the temperature pulse.
It is particularly notable that the actual temperature rise is smaller than that estimated here because part of the deposited energy is invariably utilized in ionization, dissociation, and similar processes.
This part of the energy resides in the potential form and is not completely available for heating.
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With high-LET ionizing radiations (such as fission fragments, stripped nuclei, and α-particles), the situation is somewhat different.