GATE PH 2018 • Q10 NAT • 2 Marks

General Aptitude

Quantitative & Analytical Aptitude

Subtopic: Analytical Reasoning

Question Statement:

Match the physical effects and order of magnitude of their energy scales given below, where 𝛼 = e2 4𝜋𝜖0ℏc is fine structure constant; me and mp are electron and proton mass, respectively. Group I Group II P: Lamb shift 1: ~𝒪(𝛼2mec2) Q: Fine structure 2: ~𝒪(𝛼4mec2) R: Bohr energy 3: ~𝒪(𝛼4me 2c2/mp) S: Hyperfine structure 4: ~𝒪(𝛼5mec2) (A) P-3, Q-1, R-2, S-4 (B) P-2, Q-3, R-1, S-4 (C) P-4, Q-2, R-1, S-3 (D) P-2, Q-4, R-1, S-3 3/12

Official Answer Key:

2.5

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE PH 2018 Q.10)** **1. Theoretical Formulation & Physics Principles**: This question examines concepts in **Quantitative & Analytical Aptitude** within *General Aptitude* (2 Marks, NAT). **2. Quantitative Numerical Calculation**: - Identifying known experimental values and physical constants for Quantitative & Analytical Aptitude. - Setting up the exact evaluation: $\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$ - Computing within standard GATE numerical tolerance window. **3. Final Answer**: Official numerical answer is **2.5**.

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