The energy vs. wave vector k E relationship near the bottom of a band for a solid can be
approximated as 42 ) ( ) (ka B ka A E , where the lattice constant a = 2.1 Å. The values of A and
B are J, 10 2 . 3 and J 10 3 . 62019 respectively. At the bottom of the conduction band, the ratio
of the effective mass of the electron to the mass of free electron is _______. (Give your answer
upto two decimal places)
(Take =1.05x10-34 J-s, mass of free electron= 9.1x10-31 kg)
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2016 Q.39)**
**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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