# Strontium-90 has a half-life of 28.5 years. How long (in years) will it take for 94.9900% of the strontium-90 released in a nuclear reactor accident to disappear?

Jun 1, 2018

123 years, to three significant figures

#### Explanation:

94.99% of a quantity gone means that 5.01% is left, or, fractionally, 0.0501 of it.

When one half-life has elapsed, 0.5 of it is left. The question is how many halvings leave us with 0.0501, i.e. find $x$ where ${0.5}^{x} = 0.0501$.

This is a logarithmic problem:
$\log {0.5}^{x} = \log 0.0501$
$x \log 0.5 = \log 0.0501$
$x = \log \frac{0.0501}{\log} 0.5 = 4.319 \ldots$ half lives.

For a half life of 28.5 years, this is (to three significant figures) 123 years.