The Fermi energies of two metals X and Y are 5 eV and 7 eV and their Debye temperatures are 170
K and 340 K, respectively. The molar specific heats of these metals at constant volume at low
temperatures can be written as 3T A TC XXXV and ,3T A T CYYYV where γ and A
are constants. Assuming that the thermal effective mass of the electrons in the two metals are same,
which of the following is correct?
(A) 8 ,5
7
Y
X
Y
X
A
A
(B) 8
1,5
7
Y
X
Y
X
A
A
(C) 8
1,7
5
Y
X
Y
X
A
A
(D) 8 ,7
5
Y
X
Y
X
A
A
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2016 Q.45)**
**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**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.