Strontium Bone

26Sep/08Off

Strontium Bone

Please help me with the chemistry/calculus problem?

The half-life of radioactive strontium-90 is approximately 30 years. In 1960, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 5 percent of the original amount absorbed remains?

General decay equation: A(t) = A*e^(-kt), where A is the starting amount, t is time in years, and k is the decay constant.

To find k, replace A(t) with A/2, half the original amount, and t with 30, then solve for k.

You get k = (ln 2) / 30 = 0.0231049

So the equation for this problem is A(t) = A*e^(-0.0231049t)

To find how long until 5% remains, let A(t) = .05A and solve for t:

.05A = A*e^(-0.0231049t)
.05 = e^(-0.0231049t)
ln(.05) = -0.0231049t
ln(.05) / -0.0231049 = t = 129.66 years.