Explain why the half-life of a radioactive isotope is independent of the temperature of the sample and of the chemical compound in which the isotope is found.

Radioactive decay is a nuclear process that occurs within the nucleus of an atom. The probability of a nucleus decaying per unit time – the decay constant – is determined solely by the nuclear structure and the energy balance of that particular nuclide. Temperature only changes the kinetic energy of the atoms and the energies of the outer‑shell electrons; it does not alter the internal nuclear forces or the binding energy of the nucleus. Likewise, chemical bonding involves only the outermost electrons and has no influence on the nuclear structure or the forces that hold the nucleus together. Because the decay constant depends only on the nucleus itself, the half‑life, which is related to the decay constant by (t_{1/2}=0.693/lambda), is independent of both temperature and the chemical compound in which the isotope is found.