Question

Thallium-207 decays exponentially with a half life of 4.5 minutes. if the initial amount of the isotope was 28 grams, how many grams of the isotope will remain after 7 minutes?

Answer 1

An exponential decay law has the general form: A = Ao * e ^ (-kt) =>

A/Ao = e^(-kt)

Half-life time => A/Ao = 1/2, and t = 4.5 min

=> 1/2 = e^(-k*4.5) => ln(2) = 4.5k => k = ln(2) / 4.5 ≈ 0.154

Now replace the value of k, Ao = 28g  and t = 7 min to find how many grams of Thalium-207 will remain:

A = Ao e ^ (-kt) = 28 g * e ^( -0.154 * 7) = 9.5 g

Answer 9.5 g.