To determine the binding energy of a mole of nuclei with a given mass defect, we will use Einstein's famous mass-energy equivalence formula:
[tex]\[ E = mc^2 \][/tex]
where:
- [tex]\( E \)[/tex] is the energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( c \)[/tex] is the speed of light in a vacuum (approximately [tex]\( 3 \times 10^8 \)[/tex] meters per second).
Given:
- Mass defect, [tex]\( m = 0.00084 \)[/tex] kilograms per mole,
- Speed of light, [tex]\( c = 3 \times 10^8 \)[/tex] meters per second.
Let's compute the binding energy, [tex]\( E \)[/tex]:
[tex]\[ E = mc^2 \][/tex]
Substitute the given values:
[tex]\[ E = (0.00084 \text{ kg/mol}) \times (3 \times 10^8 \text{ m/s})^2 \][/tex]
First, compute the speed of light squared:
[tex]\[ (3 \times 10^8)^2 = 9 \times 10^{16} \text{ (m/s)}^2 \][/tex]
Now, multiply this with the mass defect:
[tex]\[ E = 0.00084 \text{ kg/mol} \times 9 \times 10^{16} \text{ J/kg} \][/tex]
[tex]\[ E = 0.00084 \times 9 \times 10^{16} \text{ J/mol} \][/tex]
[tex]\[ E = 7.56 \times 10^{13} \text{ J/mol} \][/tex]
Therefore, the binding energy of a mole of nuclei with a mass defect of 0.00084 kilograms per mole is:
[tex]\[ \boxed{7.56 \times 10^{13} \text{ J/mol}} \][/tex]
So, the correct answer is:
[tex]\[ \text{B. } 7.56 \times 10^{13} \text{ J/mol} \][/tex]
