The half-life of tritium is 12.5 years. What mass of tritium of initial mass 64 mg will remain undecayed after 50 years?

Options

A. 32 mg
B. 8 mg
C. 16 mg
D. 4 mg

Answer

To solve the problem of how much tritium remains undecayed after 50 years, given that the half-life of tritium is 12.5 years and the initial mass is 64 mg, we can follow these steps:

### Step-by-Step Solution:

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

2. **Determine the Number of Half-Lives in 50 Years**:
To find out how many half-lives fit into 50 years, we divide the total time by the half-life:
\[ \text{Number of half-lives} = \frac{50 \text{ years}}{12.5 \text{ years}} = 4 \]
This means that 50 years is equivalent to 4 half-lives.

3. **Calculate the Remaining Mass After Each Half-Life**:
We start with an initial mass of 64 mg and apply the half-life reduction for each of the 4 half-lives:
- After 1st half-life (12.5 years):
\[ \text{Remaining mass} = \frac{64 \text{ mg}}{2} = 32 \text{ mg} \]
- After 2nd half-life (25 years):
\[ \text{Remaining mass} = \frac{32 \text{ mg}}{2} = 16 \text{ mg} \]
- After 3rd half-life (37.5 years):
\[ \text{Remaining mass} = \frac{16 \text{ mg}}{2} = 8 \text{ mg} \]
- After 4th half-life (50 years):
\[ \text{Remaining mass} = \frac{8 \text{ mg}}{2} = 4 \text{ mg} \]

4. **Final Answer**:
After 50 years, the remaining mass of tritium is **4 mg**.

### Summary of the Calculation:
- Initial mass: 64 mg
- After 1 half-life (12.5 years): 32 mg
- After 2 half-lives (25 years): 16 mg
- After 3 half-lives (37.5 years): 8 mg
- After 4 half-lives (50 years): 4 mg

Thus, the final answer is **4 mg**.

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