# Thread: Half-life problem

1. ## Half-life problem

The half-life of radioactive strontium-90 is approximately 32 years. In 1964, 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?

2. Originally Posted by cwarzecha
The half-life of radioactive strontium-90 is approximately 32 years. In 1964, 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?
You have
$\displaystyle A(t) = A_0 \left ( \frac{1}{2} \right )^{t/t_{1/2}}$
where $\displaystyle t_{1/2} = 32$. We are looking for 5% to be left so we know that
$\displaystyle \frac{A(t)}{A_0} = 0.05$

So solve
$\displaystyle \frac{A(t)}{A_0} = 0.05 = \left ( \frac{1}{2} \right )^{t/32}$

-Dan

### how long will it take until only 25 percent of the strontium 90 remains

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