Plutonium-240 decays according to the function / [Q (t) = Q _{o}e ^{-kt}/] where Q represents the quantity remaining after t years and k is the decay constant, 0.00011 ... How long will it take 36 grams of plutonium-240 to decay to 12 grams?. A. 18,900 years. B. 1.44 years. C. 9,990 years. D. 2,100 years.

Question

Chemistry

Andrew

29 June, 23:30

Plutonium-240 decays according to the function / [Q (t) = Q _{o}e ^{-kt}/] where Q represents the quantity remaining after t years and k is the decay constant, 0.00011 ... How long will it take 36 grams of plutonium-240 to decay to 12 grams?. A. 18,900 years. B. 1.44 years. C. 9,990 years. D. 2,100 years.

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Answers (2)

Know the Answer?

Ximena Shah · Answer 1

C. 9,990 years is the correct answer

Wade Kelley · Answer 2

To answer the question above, substitute the given values to the given equation,

Q (t) = Q x e^-kt

12 grams = (36 grams) x e^ (-0.00011) (t)

Solving for t gives t = 9,987.38 years or approximately equal to 9,990 years. Thus, the answer is letter C.