Problema Solution
In two years, 20% of a radioactive element decays. Find its half-life. (Give your answer correct to 1 decimal place.)
Answer provided by our tutors
The amount A of the radioactive material present at a time t is given by the model
A = A0*(1/2)^(t/h)
where A0 is the amount present initially, h is the half-life of the material.
In our case we have A = A0 - 0.20A0 = 0.80*A0 and t=2, we need to find h
0.80*A0 = A0*(1/2)^(2/h) dive both sides by A0
(1/2)^(2/h) = 0.80
(2/h) log (1/2) = log (0.80)
by solving we find
h = 6.2 hr
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the half-life is 6.2 hours.