Question

Nuclei \(A\) and \(B\) form a nucleus \(C\). Binding energy per nucleon for \(A, B\) and \(C\) are \(3\,\text{MeV}, 7\,\text{MeV}\) and \(6\,\text{MeV}\) respectively. Find the energy produced in the reaction: \[ 2A^{3} + B^{4} \rightarrow C^{10} \]

• A. \(12\,\text{MeV}\)
• B. \(14\,\text{MeV}\)
• C. \(13\,\text{MeV}\)
• D. \(15\,\text{MeV}\)

Answer 1

The Correct Option is B

Concept:
Energy released in a nuclear reaction equals the difference between the total binding energy of the products and the total binding energy of the reactants. \[ Q = BE_{\text{products}} - BE_{\text{reactants}} \] Binding energy of a nucleus: \[ BE = (\text{Binding energy per nucleon}) \times (\text{Number of nucleons}) \] Step 1: Calculate total binding energy of reactants. For nucleus \(A^3\): \[ BE = 3 \times 3 = 9\,\text{MeV} \] Since there are two \(A\) nuclei: \[ BE_{A} = 2 \times 9 = 18\,\text{MeV} \] For nucleus \(B^4\): \[ BE_{B} = 4 \times 7 = 28\,\text{MeV} \] Total binding energy of reactants: \[ BE_{\text{LHS}} = 18 + 28 = 46\,\text{MeV} \] Step 2: Calculate total binding energy of product. For nucleus \(C^{10}\): \[ BE_{\text{RHS}} = 10 \times 6 = 60\,\text{MeV} \] Step 3: Calculate energy released. \[ Q = BE_{\text{RHS}} - BE_{\text{LHS}} \] \[ Q = 60 - 46 \] \[ Q = 14\,\text{MeV} \]