Our justification for that assumption is that most of the radiation comes from the sun, and the sun has been shining with apparently constant brightness for the last few thousand years of human history. Although sunspots might cause daily fluctuations in radiation that increase and decrease every 11 years or so, over centuries, the average amount of radiation remains the same. If the atmosphere started out with absolutely no 14 C, there would be a certain amount after one year of exposure of nitrogen to cosmic radiation. The birth rate is constant. How Carbon 14 Dies Stable carbon has six protons and six neutrons.
Stable nitrogen has seven protons and seven neutrons.
Stable oxygen has eight protons and eight neutrons. But 14 C is not so well balanced. It has six protons and eight neutrons, which makes it unstable. Sooner or later, one of the neutrons spits out an electron and becomes a proton. This gives it seven protons and seven neutrons, which makes it nitrogen.