Question

Calculate the disintegration energy Q for the fission of ${}^{\mathbf{52}}\mathit{C}\mathit{r}$into two equal fragments. The masses you will need are

role="math" localid="1661753124790" ${}^{\mathbf{52}}\mathit{C}\mathit{r}\mathbf{}\mathbf{}\mathbf{51}\mathbf{.}\mathbf{94051}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}{}^{\mathbf{26}}\mathit{M}\mathit{g}\mathbf{}\mathbf{}\mathbf{}\mathbf{25}\mathbf{.}\mathbf{98259}\mathit{u}\mathbf{}\mathbf{}$

Short answer

The disintegrated energy is $-23\mathrm{MeV}$.

Step-by-step solution

Given data

The mass of ${}^{52}Cr,m_{cr}=51.94051u$

The mass of${}^{26}Mg,m_{Mg}=25.98259u$

Determine the formula to calculate the disintegrated energy.

The expression to calculate the disintegrated energy is given as follows.

$$\begin{gathered} \mathit{Q}\mathbf{=}\mathbf{‐}\mathbf{∆}\mathit{m}{\mathit{c}}^{\mathbf{2}} \\ \mathit{Q}\mathbf{=}\left(m_{Cr}‐2m_{Mg}\right){\mathit{c}}^{\mathbf{2}} \end{gathered}$$ ...(i)

Calculate the value of disintegrated energy.

Consider the fission reaction as given follow.

${}^{52}Cr\to {}^{26}Mg+{}^{26}Mg$

Calculate the disintegrated energy.

Substitute$51.94051u$ for $m_{Cr}$,$25.98259u$ for $M_{Mg}$and$931.5MeV/u$ for$c^2$ into equation (i).

$$\begin{gathered} Q=\left(51.9405\mathrm{u}-2\times 25.98259\mathrm{u}\right)931.5\mathrm{MeV}/\mathrm{u} \\ Q=-0.02467\times 931.5\mathrm{MeV} \\ Q=-23\mathrm{MeV} \end{gathered}$$

Hence the disintegrated energy is $-23\mathrm{MeV}$.