After three half lives, the percentage of fraction of amount

Options

A. 6.35
B. 12.5
C. 50
D. 75

Explanation

To solve the problem of determining the percentage of the remaining amount of a radioactive substance after three half-lives, we can follow these steps:

### Step 1: Understand the Concept of Half-Life
The half-life of a radioactive substance is the time required for half of the substance to decay. After each half-life, the amount of the substance is reduced by half.

### Step 2: Identify the Formula
The formula to calculate the remaining amount of a radioactive substance after a certain number of half-lives is:
\[ C = \frac{C_0}{2^n} \]
Where:
- \( C \) = remaining amount after \( n \) half-lives
- \( C_0 \) = initial amount (starting amount)
- \( n \) = number of half-lives

### Step 3: Set Initial Conditions
For this problem, we can assume the initial amount \( C_0 \) is 100% (or 100 units for simplicity). The number of half-lives \( n \) is given as 3.

### Step 4: Substitute Values into the Formula
Now, we can substitute the values into the formula:
\[ C = \frac{100}{2^3} \]

### Step 5: Calculate \( 2^3 \)
Calculate \( 2^3 \):
\[ 2^3 = 8 \]

### Step 6: Calculate the Remaining Amount
Now substitute back into the equation:
\[ C = \frac{100}{8} = 12.5 \]

### Step 7: Interpret the Result
The remaining amount after three half-lives is 12.5% of the original amount.

### Final Answer
After three half-lives, the percentage of the remaining amount of the radioactive substance is **12.5%**.

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