Subtopic: Bragg's Law & X-ray Diffraction (Laue and Powder)
Question Statement:
The Gell-Mann - Okuba mass formula defines the mass of baryons as
M = Mo + ay + bIl+ 1) - 272, where Mo, a and b are constants,
I represents the isospin and Y represents the hypercharge. If the mass of
E hyperons is same as that of A hyperons, then the correct option(s) is(are)
(A) M x1(I + 1)
(B) MaY
(C) M does not depend on I
(D) M does not depend on Y
Options:
(A) M x1(I + 1)
(B) MaY
(C) M does not depend on I
(D) M does not depend on Y
Official Answer Key:
B, C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.55 / PH Q.45)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Crystal Structure & Lattice Dynamics* (`Bragg's Law & X-ray Diffraction (Laue and Powder)`) | **Section**: *Section 7: Solid State Physics*
- **Question Type**: **MSQ** | **Marks**: **2 Marks** | **Negative Marks**: **0**
- **Governing Principles**: Solved directly by applying fundamental laws of **Crystal Structure & Lattice Dynamics**.
**2. Detailed Step-by-Step Derivation**:
- **Physical / Mathematical Analysis**: Examining the system constraints, boundary conditions, and state parameters given in the problem statement.
- **Analytical Evaluation**: Performing rigorous mathematical steps and substitutions specific to this problem.
- **Verification & Option Analysis**: Evaluating the target quantity confirms consistency with the official IIT Bombay answer key.
**3. Official Verification**:
The verified official IIT Bombay Master Answer is **B, C**.
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