# Age calculation carbon dating

To convert grams to a number of atoms, divide by the atomic mass of carbon-14 and multiply by Avagadro's number, 6.02 x 10 atoms That's 520 billion atoms of carbon-14. Let's convert that to seconds and divide by ln(2), the natural logarithm of 2 (0.693), to get the average lifetime of carbon-14 atoms: average lifetime: 5,700 years x (365 days/year) x (24 hours/day) x (60 minutes/hour) x (60 seconds/minute) / 0.693 = 2.6 x 10 per second) = 2.0 atoms per second = 2.0 becquerels That's 2 atoms per second.

The resulting decay product is a normal nitrogen-14 atom, with 7 protons and 7 neutrons in the nucleus.

The only natural fresh source of carbon-14 is from the action of cosmic rays on atmospheric nitrogen. The nitrogen nucleus contains 7 protons and 7 neutrons.

When a cosmic ray in the form of a neutron strikes an atmospheric nitrogen nucleus, it can knock out and replace a proton.

The carbon-14 undergoes radioactive decay once the plant or animal dies, and measuring the amount of carbon-14 in a sample conveys information about when the plant or animal died.

A sample of wood taken from a freshly felled tree contains 10 grams of carbon.

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For example, from a sample containing 10 grams of carbon, if you detect 1.0 atoms decayed per second, you can conclude that the concentration of carbon-14 has fallen by one-half, and the sample is one half-life old, or 5,700 years.

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