Half life of Oxygen factors?

We can be a bit more parsimonious in labeling the nuclide. Just call it "oxygen-15". Since it is oxygen, everyone will know it has eight protons.

Radioactive nuclides decay according to an exponential equation:

A(t) = A(0) * exp(-kt)

where A(t) is the activity at time t (and A(0) is the activity at time zero),

and k is the decay constant.

Rearranging, we get

A(t) / A(0) = exp(-kt).

What we want is to solve for A(t)/A(0) = 10^(-4).

To make things easier, we can do the same thing with the equation

A(t) / A(0) = 2^(t/T)

where T is the half-life.

So we want to know at how many half-lives we raise 2 to in order to yield a value of 5*10^(-4).

2^(-t/T) = 5*10^(-4)

Take logs of both sides.

(-t/T) * log(2) = log(5*10^(-4))

(-t/T) = log(5*10^(-4))/log(2) = -3.301/0.301= -10.97

-t/T = -t/122 = -10.97

t = 10.97 * 122 = 1338 seconds