List of top Solid State Physics Questions asked in GATE PH

Consider an atomic gas with number density \( n = 10^{20} \, \text{m}^{-3} \), in the ground state at 300 K. The valence electronic configuration of atoms is \( f^7 \). The paramagnetic susceptibility of the gas \( \chi = m \times 10^{-11} \). The value of \( m \) (rounded off to two decimal places) is \(\underline{\hspace{2cm}}\). 
(Given: Magnetic permeability of free space \( \mu_0 = 4\pi \times 10^{-7} \, \text{H m}^{-1} \), Bohr magneton \( \mu_B = 9.274 \times 10^{-24} \, \text{A m}^2 \), Boltzmann constant \( k_B = 1.3807 \times 10^{-23} \, \text{K}^{-1} \))

As shown in the figure, inverse magnetic susceptibility \( \frac{1}{\chi} \) is plotted as a function of temperature (T) for three different materials in paramagnetic states. 

(Curie temperature of ferromagnetic material = \( T_C \), Néel temperature of antiferromagnetic material = \( T_N \))
Choose the correct statement from the following 
 

The free energy of a ferromagnet is given by \[ F = F_0 + a_0 (T - T_C) M^2 + b M^4, \] where \(F_0\), \(a_0\), and \(b\) are positive constants, \(M\) is the magnetization, \(T\) is the temperature, and \(T_C\) is the Curie temperature. The relation between \(M^2\) and \(T\) is best depicted by 

A two-dimensional square lattice has lattice constant \(a\). \(k\) represents the wavevector in reciprocal space. The coordinates \((k_x, k_y)\) of reciprocal space where band gap(s) can occur, are 
 

As shown in the figure, X-ray diffraction pattern is obtained from a diatomic chain of atoms P and Q. The diffraction condition is given by \( a \cos \theta = n\lambda \), where \( n \) is the order of the diffraction peak. Here, \( a \) is the lattice constant and \( \lambda \) is the wavelength of the X-rays. Assume that atomic form factors and resolution of the instrument do not depend on \( \theta \). Then, the intensity of the diffraction peaks is 

Choose the graph that best describes the variation of dielectric constant (\( \epsilon_r \)) with temperature (\( T \)) in a ferroelectric material. 
(T\(_C\) is the Curie temperature)