Tritium has a half-life of 12.5 yr undergoing `beta` decay .Fraction of sample remaining undecayed after 25 yr will be

Options

A. `1/8`
B. `1/2`
C. `1/4`
D. `1/16`

Answer

To solve the problem of finding the fraction of tritium remaining undecayed after 25 years, we can follow these steps:

### Step 1: Understand the Half-Life Concept
The half-life of a radioactive substance is the time required for half of the substance to decay. For tritium, the half-life is given as 12.5 years.

### Step 2: Determine the Number of Half-Lives
To find out how many half-lives fit into the total time of 25 years, we can divide the total time by the half-life:
\[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{25 \text{ years}}{12.5 \text{ years}} = 2 \]

### Step 3: Calculate the Remaining Fraction
After each half-life, the remaining fraction of the substance can be calculated using the formula:
\[ \text{Remaining fraction after } n \text{ half-lives} = \left(\frac{1}{2}\right)^n \]
For 2 half-lives:
\[ \text{Remaining fraction} = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \]

### Step 4: Conclusion
Thus, the fraction of the tritium sample that remains undecayed after 25 years is:
\[ \frac{1}{4} \]

### Final Answer
The fraction of the sample remaining undecayed after 25 years is \(\frac{1}{4}\).

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