A particle of unit mass moves in a potential V(r) = -Veିమ
. If the angular
momentum of the particle is L = 0.5ඥV , then which of the following statements
are true?
Options:
(A) There are two equilibrium points along the radial coordinate
(B) There is one stable equilibrium point at rଵ and one unstable equilibrium point at
rଶ > rଵ
(C) There are two stable equilibrium points along the radial coordinate
(D) There is only one equilibrium point along the radial coordinate
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.49)**
**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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