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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Question:

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.

Answer:

The time taken for the 36 grams of Plutonium-240 to decay to 12 grams is 999 years (Option C)

Data obtained from the question

  • Original amount (Q₀) = 36 g
  • Decay constant (K) = 0.00011 /year
  • Amount remaining (Q) = 12 g
  • Time (t) = ?

How to determine the time

The time taken for the Plutonium-240 to decay from 36 g to 12 g can be obtained as illustrated below:

Q = Q₀e^(–kt)

12 = 36 × e^(–0.00011 × t)

Divide both sides by 36

e^(–0.00011 × t) = 12 / 36

Take the Ln of both sides

–0.00011 × t = Ln (12/36)

Divide both sides by–0.0001

t = [Ln (12/36)] / –0.00011

t = 9990 years

Learn more about half life:

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