Subtopic: Binding Energy Curve & Semi-Empirical Mass Formula
Question Statement:
Binding energy and rest mass energy of a two-nucleon bound state are denoted by
B and mc2, respectively, where c is the speed of light . The minimum energy of a
photon required to dissociate the bound state is
Options:
(A) B
(B) B (1 + B
2mc2)
(C) B (1 - B
2mc2)
(D) B - mc2
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2024 Q.36)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *Section 9: Nuclear and Particle Physics* | **Topic**: *Nuclear Properties & Nuclear Forces* (`Binding Energy Curve & Semi-Empirical Mass Formula`)
- **Question Type**: **MCQ** | **Marks**: **2 Marks**
- **Theoretical Framework**: Governed by foundational physical principles in **Nuclear Properties & Nuclear Forces** (`Binding Energy Curve & Semi-Empirical Mass Formula`).
**2. Step-by-Step Physical Derivation**:
- **Step 1 (Physical Principles & Boundary Conditions)**: Identify the applicable conservation laws (energy, momentum, angular momentum, charge), boundary conditions, or Hamiltonian/Lagrangian formalisms.
- **Step 2 (Mathematical Formalism & Equations of Motion)**: Formulate the governing differential equations, operator eigenvalue relations, or tensor transformations corresponding to the specified physical geometry.
- **Step 3 (Algebraic & Numerical Substitution)**: Substitute the system parameters into the derived formalism and evaluate the expressions step-by-step.
- **Step 4 (Final Evaluation)**: Arrive at the exact numerical magnitude or analytic formula: **B**.
**3. Official Verification & Conclusion**:
The verified official IIT Master Answer is **Option (B): `B (1 + B
2mc2)`**.
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