One microgram of matter converted into energy will give.

Options

A. `9xx10^ 7J`
B. `9xx10^ 3J`
C. `9xx10^ (10)J`
D. `9xx10^ 5J`

Answer

To solve the problem of how much energy is produced when one microgram of matter is converted into energy, we can use Einstein's famous equation:

### Step-by-Step Solution:

1. **Convert Micrograms to Kilograms**:
- Given mass = 1 microgram = \(1 \times 10^{-6}\) grams.
- To convert to kilograms, we use the conversion factor:
\[ 1 \text{ microgram} = 1 \times 10^{-6} \text{ grams} = 1 \times 10^{-9} \text{ kilograms} \]

2. **Use Einstein's Equation**:
- Einstein's equation is given by:
\[ E = mc^2 \]
- Where:
- \(E\) = energy in joules,
- \(m\) = mass in kilograms,
- \(c\) = speed of light in a vacuum (approximately \(3 \times 10^8\) m/s).

3. **Substitute the Values**:
- Substitute \(m = 1 \times 10^{-9}\) kg and \(c = 3 \times 10^8\) m/s into the equation:
\[ E = (1 \times 10^{-9} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]

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

5. **Calculate the Energy**:
- Now substitute \(c^2\) back into the energy equation:
\[ E = (1 \times 10^{-9}) \times (9 \times 10^{16}) = 9 \times 10^{7} \text{ joules} \]

6. **Final Result**:
- Therefore, the energy produced from the conversion of one microgram of matter into energy is:
\[ E = 9 \times 10^{7} \text{ joules} \]

### Answer:
The energy produced when one microgram of matter is converted into energy is \(9 \times 10^{7}\) joules.

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