Question 13

 Suppose there were a greater number of carbon ¹⁴₆C atoms in a plant living 5000 yr ago than is currently believed. When the seeds of this plant are tested today using radiocarbon dating, is the age obtained too small or too large? Give your reasoning.

SOLUTION: Too small. The number of carbon-14 atoms decays exponentially (like a capacitor discharging-you can think of the decay constant as analogous to the inverse of the time constant in RC circuits). Say the date is based on some number of atoms, and it takes some time for the number of atoms to decay to the present quantity. Now, if there were actually more atoms originally, then it would take longer to decay down to the present number of atoms. That is, the sample would need to be older. Hence our estimate would be too small.