Plutonium decays with half life of 24000 years. If plutonium is stored for 72000 years, the fraction of it that remains is

Options

A. `1//8`
B. `1//3`
C. `1//4`
D. `1//2`

Explanation

To solve the problem of determining the fraction of plutonium that remains after 72,000 years, given its half-life of 24,000 years, we can follow these steps:

### Step 1: Understand the half-life concept
The half-life of a substance is the time required for half of the substance to decay. In this case, the half-life of plutonium is 24,000 years.

### Step 2: Determine the number of half-lives
To find out how many half-lives fit into the total time of storage (72,000 years), we can use the formula:
\[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} \]
Substituting the values:
\[ \text{Number of half-lives} = \frac{72000 \text{ years}}{24000 \text{ years}} = 3 \]

### Step 3: Calculate the remaining fraction
The fraction of the substance that remains after a certain number of half-lives can be calculated using the formula:
\[ \text{Fraction remaining} = \left(\frac{1}{2}\right)^{n} \]
where \( n \) is the number of half-lives. In our case, \( n = 3 \):
\[ \text{Fraction remaining} = \left(\frac{1}{2}\right)^{3} = \frac{1}{8} \]

### Step 4: Conclusion
Thus, the fraction of plutonium that remains after 72,000 years is:
\[ \frac{1}{8} \]

### Final Answer
The fraction of plutonium that remains after 72,000 years is \( \frac{1}{8} \).

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