`1 g` of hydrogen is converted into `0.993 g` of helium in a thermonuclear reaction. The energy released is.

Options

A. `63xx10^(7)J`
B. `63xx10^(10)J`
C. `63xx10^(14)J`
D. `63xx10^(20)J`

Explanation

To solve the problem of finding the energy released when 1 g of hydrogen is converted into 0.993 g of helium, we will follow these steps:

### Step 1: Calculate the Mass Defect
The mass defect (Δm) is the difference between the initial mass and the final mass after the reaction.

\[ \Delta m = \text{Initial mass} - \text{Final mass} \]

Given:
- Initial mass = 1 g (of hydrogen)
- Final mass = 0.993 g (of helium)

Calculating the mass defect:

\[ \Delta m = 1 \, \text{g} - 0.993 \, \text{g} = 0.007 \, \text{g} \]

### Step 2: Convert Mass Defect to Kilograms
Since the energy formula requires mass in kilograms, we need to convert grams to kilograms.

\[ \Delta m = 0.007 \, \text{g} = 0.007 \times 10^{-3} \, \text{kg} = 7 \times 10^{-6} \, \text{kg} \]

### Step 3: Use Einstein's Mass-Energy Equivalence Formula
The energy released (E) can be calculated using Einstein's mass-energy equivalence formula:

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

Where:
- \( c \) = speed of light = \( 3 \times 10^8 \, \text{m/s} \)

### Step 4: Calculate the Energy Released
Substituting the values into the equation:

\[ E = (7 \times 10^{-6} \, \text{kg}) \cdot (3 \times 10^8 \, \text{m/s})^2 \]

Calculating \( c^2 \):

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

Now substituting back into the energy equation:

\[ E = 7 \times 10^{-6} \cdot 9 \times 10^{16} \]

Calculating the energy:

\[ E = 63 \times 10^{10} \, \text{J} \]

### Final Answer
The energy released is:

\[ E = 6.3 \times 10^{11} \, \text{J} \]