Knowing the number of atoms that decayed in our sample over a month, we can calculate the radiocarbon decay rate.The standard way of expressing the decay rate is called the half-life.5 It’s defined as the time it takes half a given quantity of a radioactive element to decay.Radiocarbon (carbon-14 or C) forms continually today in the earth’s upper atmosphere.And as far as we know, it has been forming in the earth’s upper atmosphere at least since the Fall, after the atmosphere was made back on Day Two of creation week (part of the expanse, or firmament, described in Genesis 1:6–8). Cosmic rays from outer space are continually bombarding the upper atmosphere of the earth, producing fast-moving neutrons (sub-atomic particles carrying no electric charge) (figure 1).1 These fast-moving neutrons collide with nitrogen-14 atoms, the most abundant element in the upper atmosphere, converting them into radiocarbon (carbon-14) atoms.The difference in the number of sand grains represents the number of carbon-14 atoms that have decayed back to nitrogen-14 since the mammoth died. The sand grains in the top bowl fall to the bottom bowl to measure the passage of time.Because we have measured the rate at which the sand grains fall (the radiocarbon decay rate), we can then calculate how long it took those carbon-14 atoms to decay, which is how long ago the mammoth died. If all the sand grains are in the top bowl, then it takes exactly an hour for them all to fall.
We can measure in the laboratory how many carbon-14 atoms are still in the skull.So if half the sand grains are in the top bowl and half in the bottom bowl, then 30 minutes has elapsed since the sand grains began falling.We can calibrate an hourglass clock by timing the falling sand grains against a mechanical or electronic clock.To measure the rate of decay, a suitable detector records the number of beta particles ejected from a measured quantity of carbon over a period of time, say a month (for illustration purposes).Since each beta particle represents one decayed carbon-14 atom, we know how many carbon-14 atoms decayed during that month.If we assume that the mammoth originally had the same number of carbon-14 atoms in its bones as living animals do today (estimated at one carbon-14 atom for every trillion carbon-12 atoms), then, because we also know the radiocarbon decay rate, we can calculate how long ago the mammoth died. This dating method is also similar to the principle behind an hourglass (figure 4).The sand grains that originally filled the top bowl represent the carbon-14 atoms in the living mammoth just before it died.After plants and animals perish, however, they no longer replace molecules damaged by radioactive decay.Instead, the radiocarbon atoms in their bodies slowly decay away, so the ratio of carbon-14 atoms to regular carbon atoms will steadily decrease over time (figure 3).If the level is constant, living plants and animals should also maintain a constant carbon-14 level in them.The reason is that, as long as the organism is alive, it replaces any carbon molecules that have decayed into nitrogen.