Radioactive Decay

Differential Equation Applications

Radioactive Decay

Radioactive elements decay at a rate proportional to the amount of the element present. If the amount present is defined as N, write the differential equation that applies.

        dN/dt = kN

Now let’s look at a problem. Most of you have probably heard of carbon-12 or carbon-14 dating used to determine how old a specimen is. Here’s how it’s done.

A piece of human bone is found at an archeological site. If 10% of the original amount of radioactive carbon-14 was present, estimate the age of the bone. The half-life of C-14 is 5600 years.

Write down what is known.