To find the mass defect of a mole of nuclei with a given binding energy, we will use Einstein's famous equation that relates energy and mass: [tex]\(E = mc^2\)[/tex]. Here [tex]\(E\)[/tex] represents the energy, [tex]\(m\)[/tex] represents the mass, and [tex]\(c\)[/tex] is the speed of light.
Given data:
- Binding energy [tex]\(E = 1.8 \times 10^{15} \text{ J/mol}\)[/tex]
- Speed of light [tex]\(c = 3 \times 10^8 \text{ m/s}\)[/tex]
We need to find the mass defect [tex]\(m\)[/tex]. Rearranging Einstein's equation to solve for mass we get:
[tex]\[m = \frac{E}{c^2}\][/tex]
Substitute the given values into this equation:
[tex]\[
m = \frac{1.8 \times 10^{15} \text{ J/mol}}{(3 \times 10^8 \text{ m/s})^2}
\][/tex]
Calculate the denominator:
[tex]\[
(3 \times 10^8 \text{ m/s})^2 = (3 \times 10^8)^2 \text{ m}^2/\text{s}^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2
\][/tex]
Next, divide the binding energy by this value:
[tex]\[
m = \frac{1.8 \times 10^{15} \text{ J/mol}}{9 \times 10^{16} \text{ m}^2/\text{s}^2}
\][/tex]
Perform the division:
[tex]\[
m = \frac{1.8}{9} \times \frac{10^{15}}{10^{16}} \text{ kg/mol} = 0.2 \times 10^{-1} \text{ kg/mol}
\][/tex]
Expressing [tex]\(0.2 \times 10^{-1}\)[/tex] in standard scientific notation, we get:
[tex]\[
m = 2.0 \times 10^{-2} \text{ kg/mol}
\][/tex]
Thus, the mass defect of a mole of nuclei with a binding energy of [tex]\(1.8 \times 10^{15} \text{ J/mol}\)[/tex] is:
[tex]\[
\boxed{2.0 \times 10^{-2} \text{ kg/mol}}
\][/tex]
Therefore, the correct answer is:
B. [tex]\(2.0 \times 10^{-2} \text{ kg/mol}\)[/tex]
