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If 250 mg of a radioactive element decays to 190 mg in 36hrs find the half-life of the element.
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The formula for the decay mass in terms of half-life is
M(t) = , (1)
where t i the time; T is the half-life time, M(t) is the current remaining mass; is initial mass.
We are given = 250 mg; t = 36 hours.; M(t) = 190 mg; We need to fint half-life T.
The basic equation (1) takes the form
190 = .
Divide both sides by 250. You will get
=
or
0.76 = .
Take logarithm base 10 of both sides
log(0.76) = .
Express T
T = = calculate and get = 90.9255 hours = 90 hours and 53 minutes (approximately).
ANSWER. Half-life is about 90 hours and 53 minutes.
