Question

When a sample of Radium-226 decays, the energy released is 7.81 ×10^-13 J.What is the mass defectA. 8.68×10^-30 kgB. 2.60×10^-21 kgC. 3.84 × 10^20 kgD. 1.15×10^29 kg

Answer 1

The mass defect and the energy released in radioactive decay are related by the following equation:

`E=mc^2`

Where:

`\begin{gathered} E=\text{ Energy} \\ m=\text{ mass} \\ c=\text{ speed of light} \end{gathered}`

We solve for the mass by dividing both sides by the square of the velocity of light:

`(E)/(c^2)=m`

The speed of light is a constant and is equal to:

`c=3*10^8(m)/(s)`

Now we replace the given values:

`(7.81*10^(-13)J)/((3*10^8(m)/(s))^2)=m`

Now we solve the square in the denominator:

`(7.81*10^(-13)J)/(9*10^(16)(m)/(s))=m`

Now we solve the operations and we get:

Therefore, the mass defect is option A.