The mass defect and the energy released in radioactive decay are related by the following equation:
[tex]E=mc^2[/tex]Where:
[tex]\begin{gathered} E=\text{ Energy} \\ m=\text{ mass} \\ c=\text{ speed of light} \end{gathered}[/tex]We solve for the mass by dividing both sides by the square of the velocity of light:
[tex]\frac{E}{c^2}=m[/tex]The speed of light is a constant and is equal to:
[tex]c=3\times10^8\frac{m}{s}[/tex]Now we replace the given values:
[tex]\frac{7.81\times10^{-13}J}{(3\times10^8\frac{m}{s})^2}=m[/tex]Now we solve the square in the denominator:
[tex]\frac{7.81\times10^{-13}J}{9\times10^{16}\frac{m}{s}}=m[/tex]Now we solve the operations and we get:
[tex]8.68\times10^{-30}\operatorname{kg}=m[/tex]Therefore, the mass defect is option A.
