GATE PH 2013 • Q61
MCQ • 2 Marks
Section 9: Nuclear and Particle Physics
Nuclear & Particle Physics
Subtopic: Nuclear Models, Radioactivity & Elementary Particles
Question Statement:
X and Y are two positive real numbers such that 6 and 8 . For which of the
following values of ሻ the function ݂ܻwill give maximum value?
Options:
-
(A) (4/3, 10/3)
-
(B) (8/3, 20/3)
-
(C) (8/3, 10/3)
-
(D) (4/3, 20/3)
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2013 Q.61)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Nuclear & Particle Physics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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