Let's solve the problem step-by-step using the formula for nuclear binding energy [tex]\(E = mc^2\)[/tex].
### Step 1: Write Down the Given Values
- Mass defect ([tex]\(m\)[/tex]): [tex]\(6.9986235 \times 10^{-29}\)[/tex] kg
- Speed of light ([tex]\(c\)[/tex]): [tex]\(3 \times 10^8\)[/tex] m/s
### Step 2: Write Down the Formula
The formula to calculate the nuclear binding energy is:
[tex]\[ E = mc^2 \][/tex]
### Step 3: Substitute the Given Values into the Formula
[tex]\[ E = (6.9986235 \times 10^{-29} \, \text{kg}) \times (3 \times 10^8 \, \text{m/s})^2 \][/tex]
### Step 4: Calculate the Energy
First, we need to square the speed of light:
[tex]\[ (3 \times 10^8 \, \text{m/s})^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \][/tex]
Next, multiply this result by the mass defect:
[tex]\[ E = 6.9986235 \times 10^{-29} \, \text{kg} \times 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \][/tex]
[tex]\[ E = 6.29876115 \times 10^{-12} \, \text{joules} \][/tex]
### Step 5: Match the Answer With the Choices
Comparing this result with the options provided:
A. [tex]\(6.3 \times 10^{-12}\)[/tex] joules
B. [tex]\(0.6352 \times 10^{-8}\)[/tex] joules
C. [tex]\(6.3 \times 10^{-8}\)[/tex] joules
D. [tex]\(21.124 \times 10^{-21}\)[/tex] joules
The correct answer is:
[tex]\[ 6.29876115 \times 10^{-12} \, \text{joules} \approx 6.3 \times 10^{-12} \, \text{joules} \][/tex]
Thus, the correct answer is:
A. [tex]\(6.3 \times 10^{-12}\)[/tex] joules.
