If `10%` of a radioactive substance decays in every 5 year, then the percentage of the substance that will have decaed in `20 years` will be .

Options

A. `40%`
B. `50%`
C. `65.6%`
D. `34.4%`

Explanation

To solve the problem of determining the percentage of a radioactive substance that decays over 20 years, given that 10% decays every 5 years, we can follow these steps:

### Step 1: Understand the decay process
We know that 10% of the substance decays every 5 years. This means that after 5 years, 90% of the original substance remains.

### Step 2: Calculate the remaining substance after 20 years
Since the decay occurs every 5 years, we can calculate how many 5-year periods are in 20 years:
\[ \text{Number of periods} = \frac{20 \text{ years}}{5 \text{ years/period}} = 4 \text{ periods} \]

### Step 3: Calculate the remaining substance after each period
After each period, 90% of the substance remains. Therefore, after 4 periods, the remaining substance can be calculated as:
\[ \text{Remaining substance} = (0.90)^4 \]

### Step 4: Perform the calculation
Calculating \( (0.90)^4 \):
\[ (0.90)^4 = 0.6561 \]

### Step 5: Calculate the percentage that has decayed
To find the percentage that has decayed, we can subtract the remaining percentage from 100%:
\[ \text{Percentage decayed} = 100\% - (0.6561 \times 100\%) \]
\[ \text{Percentage decayed} = 100\% - 65.61\% = 34.39\% \]

### Step 6: Round off the answer
Rounding off to one decimal place, we find that approximately 34.4% of the substance has decayed in 20 years.

### Final Answer
The percentage of the substance that will have decayed in 20 years is **34.4%**.

---