  The abundance and biological role of potassium suggest that its unstable
nuclide was present in all stages of terrestrial biogenesis. With its enhanced
isotopic ratio in the Archean eon, $^{40}$K may have contributed to the
special, perhaps unique, biogenetic conditions that were present in the
primitive Earth. Compared to the U and Th radionuclides, $^{40}$K has a less
disruptive radiochemical impact, which may drive a moderate, but persistent
evolution of the structural and functional properties of proto-biological
molecules. In the main $\beta$-decay route of $^{40}$K, the radiation dose
generated by an Archean solution with potassium ions can be larger than the
present background radiation on Earth by one to two orders of magnitude.
Estimates of the rates of organic molecules indirectly affected by $\beta$
decays are provided for two schematic models of the propagation of secondary
events in the solvent of prebiotic solutions. The left-handed $\beta^-$
particles emitted by $^{40}$K are the best candidates to trigger an
enantiomeric excess of L-type amino acids via weak nuclear forces in the
primitive Earth. The concentration-dependent radiation dose of $^{40}$K fits
well in dry--wet scenarios of life's origins and should be considered in
realistic simulations of prebiotic chemical pathways.
