Plutonium decays with half life time 24000 yrs. if Plutonium is stored after 72000 yrs, the fraction of it that remain (A) \((1 / 2)\) (B) \((1 / 9)\) (C) \((1 / 12)\) (D) \((1 / 8)\)

Short Answer

Expert verified
After 72,000 years, the remaining fraction of plutonium is \(\frac{1}{8}\) (Option D).

Step by step solution

01

Determine the number of half-life periods

Since 1 half-life of plutonium is 24,000 years, we will divide the total time passed, which is 72,000 years, by 24,000 years to find out the number of half-lives that have passed. Number of half-lives = 72000 yrs / 24000 yrs = 3
02

Apply the half-life formula

The half-life formula is given by: Remaining fraction = \((\frac{1}{2})^n\), where n is the number of half-lives passed.
03

Calculate the remaining fraction

Now, we can plug in the number of half-lives (n = 3) into the formula: Remaining fraction = \((\frac{1}{2})^3 = \frac{1}{8}\) So, the remaining fraction of plutonium after 72,000 years is \(\frac{1}{8}\), which corresponds to the provided option (D).

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