Subtopic: Wave Mechanics, Operators & Perturbation Theory
Question Statement:
Potassium metal has electron concentration of 1.4 × 10ଶ଼m3 and the
corresponding density of states at Fermi level is 6.2 × 10ସ Joule1 m3. If the
Pauli paramagnetic susceptibility of Potassium is n × 10ି in standard scientific
form, then the value of k (an integer) is __________ (Magnetic moment of
electron is 9. 3 × 10ିଶସ Joule T1; permeability of free space is 4𝜋 × 10ି T m
A1)
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.29)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Quantum Mechanics** within *Section 4: Quantum Mechanics* (1 Mark, 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**.
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