In a nuclear explosion, one kg uranium was used. Calculate the energy released during the explosion if mass defect involved in the fusion is 0.2%.

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the mass defect
The mass defect is given as 0.2% of the total mass of uranium used. We can calculate this as follows:

\[ \text{Mass defect} = \frac{0.2}{100} \times 1 \, \text{kg} = 0.002 \, \text{kg} = 2 \times 10^{-3} \, \text{kg} \]

### Step 2: Use Einstein's mass-energy equivalence formula
According to Einstein's mass-energy equivalence principle, the energy released (E) due to the mass defect (Δm) can be calculated using the formula:

\[ E = \Delta m \cdot c^2 \]

where \(c\) is the speed of light in a vacuum, approximately \(3 \times 10^8 \, \text{m/s}\).

### Step 3: Substitute the values into the formula
Now, we substitute the mass defect and the speed of light into the equation:

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

Calculating \(c^2\):

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

### Step 4: Calculate the energy released
Now we can calculate the energy:

\[ E = 2 \times 10^{-3} \, \text{kg} \cdot 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \]

\[ E = 18 \times 10^{13} \, \text{J} \]

### Step 5: Final answer
Thus, the energy released during the explosion is:

\[ E = 1.8 \times 10^{14} \, \text{J} \quad \text{(or } 18 \times 10^{13} \, \text{J)} \]