Question

Use the graph of binding energy to estimate the total energy released if three 4 He nuclei fuse together to form a 12 C nucleus

Short answer

From the figure 42.6, plot binding energy per nucleon verse mass number given in the text book, the binding energy per nucleon for 4 nucleus approximately is 7.2 MeV and the binding energy per nucleon for 12C nucleus is 7.7MeV.

Step-by-step solution

∆E4He=47.2 MeV            = 28.8MeVThe total binding energy of three4He nuclei is,∆E1=328.8 MeV         =86.4 MeVThe nuclei C12 has 12 nucleons, so the total binding energy of  C12 nucleus is∆E2=127.7 MeV         =92.4 Mev  

The nucleus ⁴He has 4 nucleons, so the total binding energy of one ⁴He nucleus is,

Step 2

The amount of energy released in the nuclear reaction which involves three ⁴He nuclei together form a ¹²C nucleus is,

$$\begin{gathered} ∆\mathrm{E}={\mathrm{E}}_2-{\mathrm{E}}_1 \\ =92.4\mathrm{MeV}-86.4\mathrm{MeV} \\ =6.0\mathrm{MeV} \\ \mathrm{Therefore},\mathrm{the}\mathrm{amount}\mathrm{of}\mathrm{energy}\mathrm{release}\mathrm{is}6.0\mathrm{MeV} \end{gathered}$$