For the energy dispersion of an electron in a one-dimensional solid
E(k) = E0 - 2𝛾 cos(ka), the ratio of the effective mass of the electron in the solid to the
free electron mass (me) at k = 0 is R0. Taking 𝛾 = 0.5 eV and a = 0.5 nm, the value of R0
(rounded off to two decimal place) is _____
(ℏ = 1.054 × 10-34 J. s, me = 9.1 × 10-31 kg, electron charge = 1.6 × 10-19 C)
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.32)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (1 Mark, 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**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.