0.157 fraction of a sample of 6832ge, whose half-life is about 9 months, will remain after 3.5 yr.
Solution:
The half-life of 9 months is 0.75 years.
2.0 years is 2.0/0.75 = 2.67 half-lives.
Each half-life represents a reduction in the amount remaining by a factor of two, so: A(t)/A(0) = 2^(-t/h)
where A(t) = amount at time t
h = half-life in some unit
t = elapsed time in the same unit
A(t)/A(0) = 2^(-2.67) = 0.157
15.7% of the original amount will remain after 2.0 years.
The half-life is the time required for a quantity to fall to half of its starting value. The expression is commonly used in nuclear physics to describe how quickly unstable atoms decay radioactively or how long stable atoms remain. The term can also be used more generally to refer to any type of exponential decay.
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