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?

1 Answer
Jun 1, 2018

Answer:

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 0.0501/log 0.5=4.319...# half lives.

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