Tritium has a half life of 12.5 years against beta decay. What fraction of a sample of pure tritium will remain undecayed after 25 years?

Options

A. one half
B. one fourth
C. one third
D. can't say

Explanation

To solve the problem of how much tritium remains undecayed after 25 years, we can follow these steps:

### Step 1: Understand the concept of half-life
The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, the half-life of tritium is given as 12.5 years.

### Step 2: Determine the time elapsed
We need to find out how much tritium remains after 25 years. Since the half-life is 12.5 years, we can see how many half-lives fit into 25 years:
\[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{25 \text{ years}}{12.5 \text{ years}} = 2 \]

### Step 3: Calculate the remaining fraction after each half-life
After each half-life, the amount of the substance remaining is halved. Starting with an initial amount \( N_0 \):
- After the first half-life (12.5 years), the remaining amount is:
\[ N_1 = \frac{N_0}{2} \]
- After the second half-life (25 years), the remaining amount is:
\[ N_2 = \frac{N_1}{2} = \frac{N_0}{2 \times 2} = \frac{N_0}{4} \]

### Step 4: Find the fraction of the original sample remaining
The fraction of the original sample that remains undecayed after 25 years is given by:
\[ \text{Fraction remaining} = \frac{N_2}{N_0} = \frac{N_0/4}{N_0} = \frac{1}{4} \]

### Conclusion
Thus, the fraction of the sample of pure tritium that will remain undecayed after 25 years is \( \frac{1}{4} \).

### Final Answer
The answer is \( \frac{1}{4} \).

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