One milligram of matter is converted into energy. The energy released will be

Options

A. `9xx10^6` J
B. `9xx10^8` J
C. `9xx10^10` J
D. `9xx10^12` J

Explanation

To find the energy released when 1 milligram of matter is converted into energy, we can use Einstein's mass-energy equivalence formula:

### Step-by-Step Solution:

1. **Identify the Mass**:
The mass given is 1 milligram. We need to convert this into kilograms for our calculations.
\[ 1 \text{ milligram} = 1 \times 10^{-3} \text{ grams} \]
\[ 1 \text{ gram} = 0.001 \text{ kg} \Rightarrow 1 \text{ milligram} = 1 \times 10^{-3} \times 10^{-3} \text{ kg} = 1 \times 10^{-6} \text{ kg} \]

2. **Use the Mass-Energy Equivalence Formula**:
According to Einstein's formula, the energy \( E \) can be calculated using:
\[ E = mc^2 \]
where \( m \) is the mass in kilograms and \( c \) is the speed of light in meters per second.

3. **Substitute the Values**:
The speed of light \( c \) is approximately \( 3 \times 10^8 \text{ m/s} \). Now, substituting the values into the equation:
\[ E = (1 \times 10^{-6} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]

4. **Calculate \( c^2 \)**:
First, calculate \( (3 \times 10^8)^2 \):
\[ (3 \times 10^8)^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

5. **Calculate the Energy**:
Now substitute \( c^2 \) back into the energy equation:
\[ E = (1 \times 10^{-6}) \times (9 \times 10^{16}) = 9 \times 10^{10} \text{ joules} \]

6. **Final Result**:
Therefore, the energy released when 1 milligram of matter is converted into energy is:
\[ E = 9 \times 10^{10} \text{ joules} \]

### Conclusion:
The energy corresponding to 1 milligram of matter is \( 9 \times 10^{10} \text{ joules} \).