Solid State Physics — Part 1 MCQs with Explanations

In simple metals , the phonon contribution to the electrical resistivity at temperature T follows specific trends based on the Debye temperature: Option A: This option is correct. Above the Debye temperature, the phonon contribution to the electrical resistivity is directly proportional to T. Below the Debye temperature, it is proportional to T 3 . This behavior is in accordance with the Debye theory of solids, which predicts these dependencies. Option B: This option is incorrect. The phonon contribution to electrical resistivity is not inversely proportional to T for all temperatures in simple metals. Option C: This option is incorrect. The phonon contribution to electrical resistivity is not independent of temperature for all temperatures in simple metals. Option D: This option is incorrect. While it states a direct proportionality above the Debye temperature, it incorrectly suggests a proportionality to T 5 below the Debye temperature. The correct dependency below the Debye temperature is T 3 , not T 5 . Therefore, this option is not accurate.

shear modulus is the correct answer to “The valence electrons do not directly determine the following property of a metal”. This question is standard in competitive examination syllabi for Solid State Physics.

$${\left( {\frac{{2Q}}{P}} \right)^{ - 6}}$$ is the correct answer to “The solid phase of an element follows van der Waals bonding with inter-atomic potential $$V\left( r \right) = - \frac{P}{{{r^6}}} + \frac{Q}{{{r^{12}}}}$$ where, P and Q are constants. The bond length can be expressed as”. This question is standard in competitive examination syllabi for Solid State Physics.

$$N\mu \tanh \left( {\frac{{\mu B}}{{{k_B}T}}} \right)$$ is the correct answer to “A system containing N non-interacting localized particles of spin $$\frac{1}{2}$$ and magnetic moment $$\mu $$ each is kept in constant external magnetic field B and in normal equilibrium at temperature T. The magnetization of the system is”. This question is standard in competitive examination syllabi for Solid State Physics.

$$\sqrt {2C\left( {\frac{1}{{{M_1}}} + \frac{1}{{{M_2}}}} \right)} $$ is the correct answer to “In a cubic crystal, atoms of mass M 1 lie on one set of planes and atoms of mass M 2 lie on planes interleaved between those of the first set. If C is the forte constant between nearest neighbour planes, the frequency of lattice vibrations for the optical phonon branch with wave vector k = 0 is”. This question is standard in competitive examination syllabi for Solid State Physics.

NaG type is the correct answer to “If the ionic radii of Mn and S are 0.80 and 0.184 nm respectively, the structure of MnS will be”. This question is standard in competitive examination syllabi for Solid State Physics.

The sample exhibits mixed states of magnetization near Hc is the correct answer to “An external magnetic field of magnitude H is applied to a type-I superconductor at a temperature below the transition point. Then which one of the following statements is not true for H less than the critical field H c”. This question is standard in competitive examination syllabi for Solid State Physics.

HCl is the correct answer to “Infrared absorption can be observed in which of the following molecules”. This question is standard in competitive examination syllabi for Solid State Physics.

3 is the correct answer to “The number of independent elastic constants in an isotropic cubic solid is”. This question is standard in competitive examination syllabi for Solid State Physics.

$$\psi \left( {\overrightarrow {\bf{r}} } \right) = u\left( {\overrightarrow {\bf{r}} } \right){e^{i.\overrightarrow {\bf{k}} .\overrightarrow {\bf{r}} }}$$ where, $$u\left( {\overrightarrow {\bf{r}} } \right) = u\left( {\overrightarrow {\bf{r}} + \overrightarrow {\bf{A}} } \right),\,\overrightarrow {\bf{A}} $$ is a lattice vector and $$\overrightarrow {\bf{k}} $$ is an arbitrary vector is the correct answer to “The Bloch theorem states that within a crystal, the wave function $$\psi \left( {\overrightarrow {\bf{r}} } \right)$$ , of an electron has the form”. This question is standard in competitive examination syllabi for Solid State Physics.

[2 2 1] is the correct answer to “In crystallographic notations, the vector $$\overrightarrow {{\bf{OP}}} $$ in the cubic cell shown in the figure is”. This question is standard in competitive examination syllabi for Solid State Physics.

$$R = \frac{L}{{A\mu e{N_0}}}\left[ {\exp \left( { - 1.0} \right) - 1} \right]$$ is the correct answer to “An extrinsic semiconductor sample of cross-section A and length L is doped in such a way that the dopping concentration varies as $${N_D}\left( x \right) = {N_0}\exp \left( { - \frac{x}{L}} \right),\,{N_0}$$ is a constant. Assume that the mobility $$\mu $$ of the majority carriers remains constant. The resistance R of the sample is given by”. This question is standard in competitive examination syllabi for Solid State Physics.

R and T is the correct answer to “Consider the Atomic Packing Factor (APF) of the following crystal structures: P. Simple cubic Q. Body centred cubic R. Face centred cubic T. Hexagonal close packed Which two of the above structures have equal APF”. This question is standard in competitive examination syllabi for Solid State Physics.

5.7 × 1014 is the correct answer to “If the number density of a free electron gas changes from 10 28 to 10 26 electron/m 3 , the value of plasma frequency (in Hz) changes from 5.7 × 10 15 to”. This question is standard in competitive examination syllabi for Solid State Physics.

the water molecule has a permanent dipole moment is the correct answer to “The dielectric constant of water is 80. However its refractive index is 1.75 invalidating the expression n = ε 1/2 . This is because”. This question is standard in competitive examination syllabi for Solid State Physics.

4.30 × 1021 is the correct answer to “Density of states of free electrons in a solid moving with an energy 0.1 eV is given by 2.15 × 10 21 e/V cm -3 . The density of states (in e/V cm -3 ) for electrons moving with an energy of 0.4 eV will be”. This question is standard in competitive examination syllabi for Solid State Physics.

finite thermal resistance is the correct answer to “In a cubic system with cell edge a, two phonons with wave vectors $${\overrightarrow {\bf{q}} _1}$$ and $${\overrightarrow {\bf{q}} _2}$$ collide and produce a third phonon with a wave. vector $${\overrightarrow {\bf{q}} _3}$$ such that $${\overrightarrow {\bf{q}} _1} + {\overrightarrow {\bf{q}} _2} = {\overrightarrow {\bf{q}} _3} + \overrightarrow {\bf{R}} $$ where, $$\overrightarrow {\bf{R}} $$ is a lattice vector. Such a collision process will lead to (a)”. This question is standard in competitive examination syllabi for Solid State Physics.

C2v; C2h, C2h is the correct answer to “The point group symmetrics of the three molecules shown in figures are respectively [ Notation C 2v = 2 mm; C 2h = 2/m; D 2h = mmm]”. This question is standard in competitive examination syllabi for Solid State Physics.

the cooper pairs cannot transfer energy to the lattice is the correct answer to “The thermal conductivity of a given material reduces, when it undergoes a transition from its normal state to the superconducting state. The reason is”. This question is standard in competitive examination syllabi for Solid State Physics.

0.383 nm is the correct answer to “Silicon has diamond structure with unit cell edge a = 0.542 nm. The interatomic separation is”. This question is standard in competitive examination syllabi for Solid State Physics.

\[{\rm{9}}{\rm{.3}}{\left( {{\rm{\dot A}}} \right)^3}\] is the correct answer to “A metal with body centred cubic (bcc) structure shows the first (i.e. smallest angle) diffraction peak at a Bragg angle of θ = 30°. The wavelength of X-ray used is 2.1\[{{\rm{\dot A}}}\] . The volume of the primitive unit cell of the metal is”. This question is standard in competitive examination syllabi for Solid State Physics.

EA > EB is the correct answer to “The temperature dependence of the electrical conductivity σ of two intrinsic semiconductors A and B is shown in the figure. If E A and E B are the band gaps of A and B respectively, which one of the following is true”. This question is standard in competitive examination syllabi for Solid State Physics.

number of unit cells is the correct answer to “In a one-dimensional Kronig-Penny model, the total number of possible wave functions is equal to”. This question is standard in competitive examination syllabi for Solid State Physics.

36 is the correct answer to “An n-type semiconductor has an electron concentration of 3 × 10 20 m -3 . If the electron drift velocity is 100 m/s in an electric field of 200 V/m, the conductivity (in $${\Omega ^{ - 1}}$$ m -1 ) of this material is”. This question is standard in competitive examination syllabi for Solid State Physics.

1 0 0 is the correct answer to “For a NaCI crystal, the cell-edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are”. This question is standard in competitive examination syllabi for Solid State Physics.

$${E_F} = \left( {\frac{{{E_v} + {E_c}}}{2}} \right) + \frac{3}{4}{k_B}T\ln \left( {\frac{{{m_h}}}{{{m_e}}}} \right)$$ is the correct answer to “An intrinsic semiconductor with mass of a hole m h , and mass of an electron m e is at a finite temperature T. If the top of the valence band energy is E v and the bottom of the conduction band energy is E c , the Fermi energy of the semiconductor is”. This question is standard in competitive examination syllabi for Solid State Physics.

zero is the correct answer to “A superconducting ring is cooled in the presence of a magnetic field below its critical temperature (T c ). The total magnetic flux that passes through the ring is”. This question is standard in competitive examination syllabi for Solid State Physics.

It is paramagnetic below Tc is the correct answer to “For a conventional superconductor, which of the following statements is not true”. This question is standard in competitive examination syllabi for Solid State Physics.

(3, 1, 1) is the correct answer to “Consider X-ray diffraction from a crystal with a face centred cubic (fcc) lattice. The lattice plane for which there is no diffraction peak is”. This question is standard in competitive examination syllabi for Solid State Physics.

1 eV is the correct answer to “The order of magnitude of the energy gap of a typical superconductor is”. This question is standard in competitive examination syllabi for Solid State Physics.

can be positive or negative is the correct answer to “The effective mass of an electron in a semiconductor”. This question is standard in competitive examination syllabi for Solid State Physics.

Silicon is a direct band gap semiconductor is the correct answer to “Which one of the following is not correct statement about semiconductors”. This question is standard in competitive examination syllabi for Solid State Physics.

negative near the top of the band is the correct answer to “The effective mass of an electron in a semiconductor can be”. This question is standard in competitive examination syllabi for Solid State Physics.

expels out its magnetic flux because the surface current induces a field in the direction opposite to the applied magnetic field is the correct answer to “A solid superconductor is placed in an external magnetic field and then cooled below its critical temperature. The superconductor”. This question is standard in competitive examination syllabi for Solid State Physics.

its susceptibility is doubled when it is cooled from 300 K to 200 K is the correct answer to “A ferromagnetic material has a Curie temperature 100 K. Then,”. This question is standard in competitive examination syllabi for Solid State Physics.

the plot of E versus k will be parabolic in the interval (-π/a) < k < (π/a) is the correct answer to “Consider the energy E in the first Brillouin zone as a function of the magnitude of the wave vector k for a crystal of lattice constant a. Then”. This question is standard in competitive examination syllabi for Solid State Physics.

Dulong-Petit: C = constant; Einstein: $$C \propto \frac{{{e^{ - a/T}}}}{{{T^2}}}$$ ; Debye: $$C \propto {\left( {\frac{T}{A}} \right)^3}$$ is the correct answer to “The lattice specific heat C of a crystalline solid can be obtained using. the Dulong-Petit model, Einstein model and Debye model. At low temperature hω ≫ k B T, which one of the following statements is true? (a and A are constants)”. This question is standard in competitive examination syllabi for Solid State Physics.

remains fixed in the optical mode and moves with the atoms in the acoustic mode is the correct answer to “A cubic cell consists of two atoms of masses m, and m 2 (m 1 > m 2 ) with m 1 and m 2 atoms situated on alternate planes. Assuming only nearest neighbour interactions, the centre of mass of the two atoms”. This question is standard in competitive examination syllabi for Solid State Physics.

$$\overrightarrow {\bf{A}} = \frac{{2\pi }}{a}\left( {{\bf{\hat x}} + {\bf{\hat y}}} \right);\,\overrightarrow {\bf{B}} = \frac{{2\pi }}{a}\left( {{\bf{\hat y}} + {\bf{\hat z}}} \right);\,\overrightarrow {\bf{C}} = \frac{{2\pi }}{a}\left( {{\bf{\hat x}} + {\bf{\hat z}}} \right)$$ is the correct answer to “The primitive translation vectors of the body centred cubic lattice are $$\overrightarrow {\bf{a}} = \frac{a}{2}\left( {{\bf{\hat x}} + {\bf{\hat y}} - {\bf{\hat z}}} \right),\,\overrightarrow {\bf{b}} = \frac{a}{2}\left( { - {\bf{\hat x}} + {\bf{\hat y}} + {\bf{\hat z}}} \right)$$ and $$\overrightarrow {\bf{c}} = \frac{a}{2}\left( {{\bf{\hat x}} - {\bf{\hat y}} + {\bf{\hat z}}} \right)$$ . The primitive translation vectors $$\overrightarrow {\bf{A}} ,\,\overrightarrow {\bf{B}} $$ and $$\overrightarrow {\bf{C}} $$ of the reciprocal lattice are”. This question is standard in competitive examination syllabi for Solid State Physics.

ionic polarizability is the correct answer to “The dielectric constant of a material at optical frequencies is mainly due to”. This question is standard in competitive examination syllabi for Solid State Physics.