The half-life of a radioactive element is 6 months. The time taken to reduce its original concentration to its 1.16 value is

Options

A. 1 years
B. 16 years
C. 2 years
D. 8 years

Explanation

To solve the problem of how long it takes for a radioactive element to reduce its original concentration to 1/16th of its value, given that its half-life is 6 months, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Half-Life**:
The half-life of a radioactive element is the time required for half of the radioactive substance to decay. In this case, the half-life is given as 6 months.

2. **Determine the Fraction Remaining**:
We need to find out how many half-lives it takes for the concentration to reduce to 1/16th of its original value. We can express this mathematically:
- After 1 half-life: \( \frac{1}{2} \)
- After 2 half-lives: \( \frac{1}{4} \)
- After 3 half-lives: \( \frac{1}{8} \)
- After 4 half-lives: \( \frac{1}{16} \)

3. **Count the Number of Half-Lives**:
From the above calculations, we see that it takes 4 half-lives to reduce the concentration to 1/16th.

4. **Calculate the Total Time**:
Since each half-life is 6 months, we can calculate the total time for 4 half-lives:
\[ \text{Total Time} = 4 \times \text{Half-life} = 4 \times 6 \text{ months} = 24 \text{ months} \]

5. **Convert Months to Years**:
To express the time in years, we convert months to years:
\[ 24 \text{ months} = 2 \text{ years} \]

### Final Answer:
The time taken to reduce the original concentration to its 1/16th value is **2 years**.

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