Subtopic: Partition Function & Thermodynamic Connection
Question Statement:
To sustain lasing action in a three-level laser as shown in the figure,
necessary conditions) is(are)
2
(A)
lifetime of the energy level 1 should be greater than that of energy level 2
(B) population of the particles in level 1 should be greater than that of level 0
(C) lifetime of the energy level 2 should be greater than that of energy level 0
(D) population of the particles in level 2 should be greater than that of level 1
Options:
(A) lifetime of the energy level 1 should be greater than that of energy level 2
(B) population of the particles in level 1 should be greater than that of level 0
(C) lifetime of the energy level 2 should be greater than that of energy level 0
(D) population of the particles in level 2 should be greater than that of level 1
Official Answer Key:
A, B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.25 / PH Q.15)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Statistical Ensembles & Partition Functions* (`Partition Function & Thermodynamic Connection`) | **Section**: *Section 5: Thermodynamics and Statistical Physics*
- **Question Type**: **MSQ** | **Marks**: **1 Mark** | **Negative Marks**: **0**
- **Governing Principles**: Solved directly by applying fundamental laws of **Statistical Ensembles & Partition Functions**.
**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 **A, B**.
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