Binding Energy of the nucleus: The energy that holds a nucleus together or the energy required to disassemble a nucleus into its constituent protons and neutrons completely is called binding energy. The energy that would be liberated by combining individual protons and neutrons into a single nucleus is called binding energy.
- The total binding energy of an element is the product of binding energy per nucleon and mass number.
- If in a reaction total binding energy of the resultant products is more than the total binding energy of the reactant products then in the reaction energy is absorbed and similarly vice-versa.
Total binding energy of \(A=E_{A}=5 \times 30=150 \mathrm{MeV}\)
Total binding energy of \(B=E_{B}=8.5 \times 60=510 \mathrm{MeV}\)
Total binding energy of \(\mathrm{C}=\mathrm{E}_{\mathrm{C}}=8 \times 90=720 \mathrm{MeV}\)
Total binding energy of \(D=E_{D}=7 \times 120=840 \mathrm{MeV}\)
Calculation of final and initial energies of elements for each of the reactions.
Reaction (a) \(D\rightarrow 2B\)
\(2 E_{B}-E_{D}=2(510)-840=180 \mathrm{MeV}\)
\(180>0\)
So energy is absorbed in this reaction.
Reaction (b)\(C\rightarrow B + A\)
\(E_{B}+E_{A}-E_{C}=510+150-720=-60 \mathrm{MeV}\)
\(-60<0\)
So energy is released in this reaction.
Reaction (c) \(B\rightarrow 2 \mathrm{~A}\)
\(2 E_{A}-E_{B}=2(150)-510=-210 \mathrm{MeV}\)
\(-210<0\)
So energy is released in this reaction.
So energy is released in (b) and (c) reaction.