Subtopic: Wave Mechanics, Operators & Perturbation Theory
Question Statement:
Consider 6 identical, non-interacting, spin
1
2 atoms arranged on a crystal lattice
at absolute temperature T. The z-component of the magnetic moment of each of
these atoms can be ± 𝜇B. If P and Q are the probabilities of the net magnetic
moment of the solid being 2𝜇B and 6𝜇B respectively, what is the value of
P
Q (in
integer)?
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.63)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Quantum Mechanics** within *Section 4: Quantum Mechanics* (2 Marks, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Quantum Mechanics.
- 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**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.