if in a nuclear fusion reaction, mass defect to 0.3% , then energy released in fusion of 1 kg mass

Options

A. `27xx10^10` J
B. `27xx10^11` J
C. `27xx10^12` J
D. `27xx10^13` J

Explanation

To solve the problem of calculating the energy released in a nuclear fusion reaction with a mass defect of 0.3%, we can follow these steps:

### Step 1: Determine the mass defect
Given that the mass defect is 0.3% of 1 kg, we can calculate it as follows:

\[ \text{Mass defect} (\Delta m) = \frac{0.3}{100} \times 1 \text{ kg} = 0.003 \text{ kg} \]

### Step 2: Use Einstein's mass-energy equivalence formula
According to Einstein's mass-energy relation, the energy released (E) is given by the formula:

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

where:
- \( \Delta m = 0.003 \text{ kg} \)
- \( c \) is the speed of light, approximately \( 3 \times 10^8 \text{ m/s} \)

### Step 3: Calculate \( c^2 \)
Now, we need to calculate \( c^2 \):

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

### Step 4: Substitute values into the energy formula
Now we can substitute the values into the energy formula:

\[ E = 0.003 \text{ kg} \times 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

### Step 5: Perform the multiplication
Calculating the above expression:

\[ E = 0.003 \times 9 \times 10^{16} = 27 \times 10^{13} \text{ joules} \]

### Step 6: Final Result
Thus, the energy released in the fusion of 1 kg mass is:

\[ E = 2.7 \times 10^{14} \text{ joules} \]

### Summary
The energy released in the fusion of 1 kg mass with a mass defect of 0.3% is \( 27 \times 10^{13} \) joules.

---