For a free electron gas in two dimensions, the variation of the density of states, NN(EE) as a function
of energy E, is best represented by
(A)
(B)
(C)
(D)
N(E)
E
N(E)
E
N(E)
E
N(E)
E
O Ď/a -Ď/a
kk
đđkk
vvkk
Ď/a -Ď/a O
k
vvkk
Ď/a -Ď/a O k
Ď/a -Ď/a O
k
vvkk
Ď/a -Ď/a O k
vvkk
PH 4/10
PH (GATE 2014)
1 PHYSICS-PH
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2014 Q.23)**
**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**.
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