If 250 mg of a radioactive element decays to 210 mg in 48 hours, find the half-life of the element. (Round your answer to the nearest whole number.)

Answer 1

t = hours

T = half life in hours

m(t) = m₀ (0.5)^t/T

m(t) / m₀ = (0.5)^t/T

ln[m(t) / m₀] = (t/T) ln0.5

T = t ln0.5 / ln[m(t) / m₀] = 48 ln0.5 / ln(210/250) hrs = 190.8 hrs

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