Part 1) After exactly 6 hours, the activity level of a sample of a particular ra

Question

Part 1) After exactly 6 hours, the activity level of a sample of a particular radioactive isotope, which decays into a stable isotope, has fallen to 30.0% of its initial value. Calculate the half-life of this isotope.

Part 2) Mantles for gas lanterns are made of thorium, because it forms an oxide that can survive being made incandescent for long periods of time. Natural thorium is almost 100% 232Th, with a half-life of 1.405 1010 y. If the average lantern mantle contains 300 mg of thorium, what is its activity?

Explanation / Answer

1)

here , let the half life is t0.5

final activity , A = 0.30 * Ao

time , t = 6 hours

as A = Ao * (0.5)^(t/t0.5)

0.30 * Ao = Ao * (0.5)^(t/t0.5)

0.30 = (0.5)^(6/t0.5)

solving for t0.5

t0.5 = 3.45 hours

the half life of the isotope is 3.45 hours

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please post seperate questions in different posts

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