If one microgram of `._92^235U` is completely destroyed in an atom bomb, the energy released will be ?

Options

A. `9xx10^6` J
B. `9xx10^7` J
C. `9xx10^8` J
D. `9xx10^5` J

Answer

To solve the problem of calculating the energy released when one microgram of \( _{92}^{235}U \) is completely destroyed in an atom bomb, we will use Einstein's mass-energy equivalence formula:

### Step-by-Step Solution:

1. **Understand the mass given**:
We are given the mass of uranium-235 as one microgram.
\[ \text{Mass} = 1 \, \mu g = 1 \times 10^{-6} \, g \]

2. **Convert micrograms to kilograms**:
Since the standard unit of mass in the SI system is kilograms, we need to convert micrograms to kilograms.
\[ 1 \, \mu g = 1 \times 10^{-6} \, g = 1 \times 10^{-9} \, kg \]

3. **Use Einstein's equation**:
According to Einstein's equation, the energy \( E \) released when a mass \( m \) is completely destroyed is given by:
\[ E = mc^2 \]
where \( c \) is the speed of light in a vacuum, approximately \( 3 \times 10^8 \, m/s \).

4. **Substitute the values into the equation**:
Now we substitute the mass and the speed of light into the equation:
\[ E = (1 \times 10^{-9} \, kg) \times (3 \times 10^8 \, m/s)^2 \]

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

6. **Calculate the energy**:
\[ E = (1 \times 10^{-9}) \times (9 \times 10^{16}) = 9 \times 10^{7} \, J \]

7. **Final Result**:
The energy released when one microgram of \( _{92}^{235}U \) is completely destroyed is:
\[ E = 9 \times 10^{7} \, J \]

### Conclusion:
The energy released will be \( 9 \times 10^{7} \, J \).

---