For a system of two bosons, each of which can occupy any of the two energy levels 0 and ε, the
mean energy of the system at a temperature T with T kB
1=β is given by
(A) βεβε
βεβε ε ε
2
2
2 1
2
- -
--
+ +
+
e e
e e (B) βεβε
βεε
22
1
- -
-
+
+
e e
e
(C) βεβε
βεβε ε ε
2
2
2
2
- -
--
+ +
+
e e
e e (D) βεβε
βεβε ε ε
2
2
2
2
- -
--
+ +
+
e e
e e
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2014 Q.40)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Nuclear & Particle Physics.
- 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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