A two-level system has energies zero and E . The level with zero energy is non-degenerate, while
the level with energy E is triply degenerate. The mean energy of a classical particle in this system
at a temperature T is
Options:
(A) T k E
T k E
B
B
e
Ee
/
/
31
(B) T k E
T k E
B
B
e
Ee
/
/
1
(C) T k E
T k E
B
B
e
Ee
/
/
1
3
(D) T k E
T k E
B
B
e
Ee
/
/
31
3
A
B
C
X
.47 A particle of rest mass M is moving along the positive x-direction. It decays into two photons 1
and 2 as shown in the figure. The energy of 1 is 1 GeV and the energy of 2 is 0.82 GeV. The
value of M (in units of GeV/c2) is ________. (Give your answer upto two decimal places)
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2016 Q.46)**
**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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