Premovic, Pavle I.
Quantum Theory / Particle Physics
June 15, 2019
Radioactive decay, mean lifetime, 238U, α-particle, escape, Geiger-Nuttall law.
We consider here the large populations of 238U nuclei and their emitted alpha particles. The main points are: (a) the minimum uncertainty in kinetic energy of these particles is roughly 10-34 MeV; (b) a time interval for which alpha particle of 238U nucleus makes one attempt to escape is approximately 10-21 second; (c) the number of the mean escape attempts is ~ 2×1038; (d) contribution of the tunneling time of 238U nucleus to the mean time and to the lifetime of each individual nuclei is negligible; (e) the sum of the lifetimes of 238U nuclei and the sum of the number of escape attempts of their alpha particles are constant. Consequently, the ratio of these two sums is also constant, and is about 10-21 second; and, (f) a new mathematical form of the Geiger-Nuttall law is derived using a very simple theoretical approach.