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

Options

A. `63 xx 10^7 J`
B. `63 xx 10^10 J`
C. `63 xx 10^14 J`
D. `63 xx 10^20 J`

Explanation

To solve the problem of calculating 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 (hydrogen) and the final mass (helium).

\[ \Delta M = \text{Initial Mass} - \text{Final Mass} = 1 \, \text{g} - 0.993 \, \text{g} = 0.007 \, \text{g} \]

### Step 2: Convert Mass Defect to Kilograms
Since energy calculations in physics typically use kilograms, we need to convert the mass defect from 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 Equation to Calculate Energy Released
According to Einstein's mass-energy equivalence principle, the energy (E) released can be calculated using the formula:

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

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

### Step 4: Calculate \(c^2\)
First, we calculate \(c^2\):

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

### Step 5: Calculate Energy
Now, substituting the values into the energy equation:

\[ E = 7 \times 10^{-6} \, \text{kg} \cdot 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \]

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

### Step 6: Final Result
Thus, the energy released during the thermonuclear reaction is:

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