To determine the binding energy of a mole of nuclei with a mass defect of [tex]\(0.00084 \, \text{kg/mol}\)[/tex], we'll use Albert Einstein's famous equation [tex]\(E = mc^2\)[/tex]. Here, [tex]\(E\)[/tex] is the binding energy, [tex]\(m\)[/tex] is the mass defect, and [tex]\(c\)[/tex] is the speed of light in a vacuum, which is approximately [tex]\(3 \times 10^8 \, \text{m/s}\)[/tex].
1. Given Data:
- Mass defect, [tex]\(m = 0.00084 \, \text{kg/mol}\)[/tex]
- Speed of light, [tex]\(c = 3 \times 10^8 \, \text{m/s}\)[/tex]
2. Determine the Binding Energy Using [tex]\(E = mc^2\)[/tex]:
Plugging in the given values:
[tex]\[
E = (0.00084 \, \text{kg/mol}) \times (3 \times 10^8 \, \text{m/s})^2
\][/tex]
3. Calculate [tex]\((3 \times 10^8 \, \text{m/s})^2\)[/tex]:
[tex]\[
(3 \times 10^8 \, \text{m/s})^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2
\][/tex]
4. Calculate the Binding Energy:
[tex]\[
E = 0.00084 \, \text{kg/mol} \times 9 \times 10^{16} \, \text{m}^2/\text{s}^2
\][/tex]
5. Perform the Multiplication:
[tex]\[
E = 7.56 \times 10^{13} \, \text{J/mol}
\][/tex]
Thus, the binding energy of a mole of nuclei with a mass defect of [tex]\(0.00084 \, \text{kg/mol}\)[/tex] is [tex]\(7.56 \times 10^{13} \, \text{J/mol}\)[/tex], which corresponds to option A.
Answer: A. [tex]\(7.56 \times 10^{13} \, \text{J/mol}\)[/tex]
