Question

What are some common mistakes students make with exponential decay?

Answer 1

A common error students make with exponential decay is thinking that a decay process will require only two half-life periods to completely convert one substance to the other substance.

For example, C-14 is converted to N-14 as it undergoes beta decay. The half life of this process is 5730 years.

Example: If a biological specimen contained 100g of C-14, how many years would be required for all of the C-14 to be converted to N-14?

The wrong answer is 11,460. At this point the amount of C-14 would be reduced to 25g, or 1/4 of the original amount.

Each half life period reduces the amount of C-14 by half, the reductions would be as follows (with -> indicated the passage of 1 half life period)

100g -> 50g -> 25g -> 12.5g -> 6.25g -> 3.125g -> etc.

So you can see that the amount of C-14 would not be reduced to 0g after the passage of two half life periods.