One microgram of matter converted into energy will give.

Options

A. `90 J`
B. `9 xx 10^3 J`
C. `9 xx 10^10 J`
D. `9 xx 10^5 J`

Explanation

To find out how much energy is produced when one microgram of matter is converted into energy, we can use Einstein's mass-energy equivalence formula:

\[ E = mc^2 \]

### Step 1: Convert micrograms to kilograms
1 microgram (µg) is equal to \( 10^{-6} \) grams. To convert grams to kilograms, we divide by 1000:

\[ 1 \, \text{µg} = 10^{-6} \, \text{g} = \frac{10^{-6}}{1000} \, \text{kg} = 10^{-9} \, \text{kg} \]

### Step 2: Use the mass-energy equivalence formula
Now we can substitute the mass into the equation \( E = mc^2 \). We know that the speed of light \( c \) is approximately \( 3 \times 10^8 \) m/s.

Substituting the values:

\[ E = (10^{-9} \, \text{kg}) \times (3 \times 10^8 \, \text{m/s})^2 \]

### Step 3: Calculate \( c^2 \)
Calculating \( c^2 \):

\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \]

### Step 4: Substitute \( c^2 \) back into the energy equation
Now substitute \( c^2 \) back into the energy equation:

\[ E = (10^{-9}) \times (9 \times 10^{16}) = 9 \times 10^{7} \, \text{J} \]

### Conclusion
Thus, the energy produced from converting one microgram of matter into energy is:

\[ E = 9 \times 10^{7} \, \text{J} \]