Solid State Physics — Part 2 MCQs with Explanations

$$\frac{C}{{T - {T_C}}}$$ , T > Tc is the correct answer to “The temperature (T) dependence of magnetic susceptibility $$\left( \chi \right)$$ of a ferromagnetic substance with Curie temperature (T c ) is given by”. This question is standard in competitive examination syllabi for Solid State Physics.

3.125 × 1022 cm-3 is the correct answer to “Metallic monovalent sodium crystallizes in body centred cubic structure. If the length of the unit cell is 4 × 10 -8 cm, the concentration of conduction electrons in metallic sodium is”. This question is standard in competitive examination syllabi for Solid State Physics.

3p - 3 is the correct answer to “For a three-dimensional crystal having N primitive unit cells with a basis of p atoms, the number of optical branches is”. This question is standard in competitive examination syllabi for Solid State Physics.

The area of the second BZ is twice that of the first BZ is the correct answer to “Which one of the following statements is not correct about the Brillouin Zones (BZ) of a square lattices with constant a”. This question is standard in competitive examination syllabi for Solid State Physics.

4 is the correct answer to “The kinetic energy of a free electron at a corner of the first Brillouin zone of a two-dimensional square lattice is larger than that of an electron at the mid-point of a side of the zone by a factor b. The value of b is”. This question is standard in competitive examination syllabi for Solid State Physics.

2.9° is the correct answer to “The distance between the adjacent atomic planes in CaCO 3 is 0.3 nm. The smallest angle of Bragg scattering for 0.03 nm X-ray is”. This question is standard in competitive examination syllabi for Solid State Physics.

A type II superconductor exhibits Meissner effect upto the second critical magnetic field (Hc2) is the correct answer to “Which one of the following statements about superconductors is not true”. This question is standard in competitive examination syllabi for Solid State Physics.

Q is for a superconductor and P for a conductor is the correct answer to “Variation of electrical resistivity $$\rho $$ with temperature T of three solids is sketched (on different scales) in the figure, as curves P, Q and R. Which one of the following statements describes the variations most appropriately”. This question is standard in competitive examination syllabi for Solid State Physics.

$$\frac{{{\hbar ^2}}}{{2A + 12Bk_0^2}}$$ is the correct answer to “The energy $$E\left( {\overrightarrow {\bf{k}} } \right)$$ of electrons of wave vector $$\overrightarrow {\bf{k}} $$ in a solid is given by $$E\left( {\overrightarrow {\bf{k}} } \right) = A{k^2} + B{k^4},$$ where A and B are constants. The effective mass of the electron at $$\left| {\overrightarrow {\bf{k}} } \right| = {k_0}$$ is”. This question is standard in competitive examination syllabi for Solid State Physics.

3 × 1013 is the correct answer to “The effective density of states at the conduction band edge of Ge is 1.04 × 10 19 cm -3 at room temperature (300 K). Ge has an optical band gap of 0.66 eV. The intrinsic carrier concentration (in cm -3 ) in Ge at room temperature (300 K) is approximately”. This question is standard in competitive examination syllabi for Solid State Physics.

The dispersion of frequency in the optical branch is smaller than that in the acoustic branch is the correct answer to “A linear diatomic lattice of lattice constant a with masses M and m (M > m) are coupled by a force constant C. The dispersion relation is given by $${\omega ^2} = C\left( {\frac{{M + m}}{{Mm}}} \right) \pm {\left[ {{C^2}{{\left( {\frac{{m + m}}{{Mm}}} \right)}^2} - \frac{{4{C^2}}}{{Mm}}{{\sin }^2}\frac{{ka}}{2}} \right]^{\frac{1}{2}}}$$ Which one of the following statements is incorrect”. This question is standard in competitive examination syllabi for Solid State Physics.

the charge carrier density only is the correct answer to “The Hall coefficient R H of sodium depends on”. This question is standard in competitive examination syllabi for Solid State Physics.

Five-fold axis is the correct answer to “Which one of the following axes of rotational symmetry is not permissible in single crystals”. This question is standard in competitive examination syllabi for Solid State Physics.

a conductor is the correct answer to “The potential in a divalent solid at a particular temperature is represented by a one-dimensional periodic model. The solid should behave electrically as”. This question is standard in competitive examination syllabi for Solid State Physics.

$$\sqrt {\frac{8}{3}} $$ is the correct answer to “The c/a ratio for an ideal hexagonal closed packed structure is”. This question is standard in competitive examination syllabi for Solid State Physics.

35.3° is the correct answer to “In a powder diffraction pattern recorded from a face centred cubic sample using X-rays, the first peak appears at 30°. The second peak will appear at”. This question is standard in competitive examination syllabi for Solid State Physics.

increases if the temperature decreases is the correct answer to “The critical magnetic field for a solid in superconducting state”. This question is standard in competitive examination syllabi for Solid State Physics.

Curve R represents an antiferromagnet and Q a paramagnet is the correct answer to “The dependences of the magnetic susceptibility $$\left( \chi \right)$$ of a material with temperature (T) can be represented by $$\chi \propto \frac{1}{{T - \theta }},$$ where θ is the Curie-Weiss temperature. The plot of magnetic susceptibility versus temperature is sketched in the figure, as curves P, Q and R with curve Q having θ = 0. Which one of the following statements is correct”. This question is standard in competitive examination syllabi for Solid State Physics.

half filled is the correct answer to “In a crystal of N primitive cells, each cell contains two monovalent atoms. The highest occupied energy band of the crystal is”. This question is standard in competitive examination syllabi for Solid State Physics.

a = 4R/√3 is the correct answer to “For a closed packed bcc structure of hard spheres, the lattice constant a is related to the sphere radius R as”. This question is standard in competitive examination syllabi for Solid State Physics.

P-3, Q-1, R-4, S-2 is the correct answer to “Match the following and choose the correct combination: Group 1 (Characteristic) Group 2 (Element) P. Atomic configuration 1s 2 , 2s 2 2p 6 , 3s 2 3p 6 1. Na Q. Strongly electropositive 2. Si R. Strongly electronegative 3. Ar S. Covalent bonding 4. Cl”. This question is standard in competitive examination syllabi for Solid State Physics.

B is more polar and it has a smaller value of ionic polarizability than that of A is the correct answer to “Two dielectric materials A and B exhibit both ionic and orientational polarizabilities. The variation of their susceptibilities $$\chi \left( { = {\varepsilon _r} - 1} \right)$$ with temperature T is shown in the figure, where $${\varepsilon _r}$$ is the relative dielectric constant. It can be inferred from the figure that”. This question is standard in competitive examination syllabi for Solid State Physics.

0.5 is the correct answer to “If the static dielectric constant of NaCl crystal is 5.6 and its optical refractive index is 1.5, the ratio of its electric polarizability to its total polarizability is”. This question is standard in competitive examination syllabi for Solid State Physics.

Paramagnetism is the correct answer to “In an insulating solid which one of the following physical phenomena is consequence of Pauli's exclusion principle”. This question is standard in competitive examination syllabi for Solid State Physics.

1 is the correct answer to “The energy of a ferromagnet as a function of magnetization M is given by F(M) = F 0 + 2(T - T c ) M 2 + M 4 , F 0 > 0 The number of minima in the function F(M) for T > T c is”. This question is standard in competitive examination syllabi for Solid State Physics.

-62.5 μV is the correct answer to “A sample of silicon of thickness 200 μm is doped with 10 23 phosphorus atoms per m 3 . If the sample is kept in a magnetic field of 0.2 Wb/m 2 and a current of 1 mA is passed through the sample, the Hall voltage produced is”. This question is standard in competitive examination syllabi for Solid State Physics.