Solid State Physics

In simple metals the phonon contribution to the electrical resistivity at temperature T is

The effective mass of an electron in a semiconductor

Which one of the following is not correct statement about semiconductors?

The effective mass of an electron in a semiconductor can be

A solid superconductor is placed in an external magnetic field and then cooled below its critical temperature. The superconductor

A ferromagnetic material has a Curie temperature 100 K. Then,

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

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

An extrinsic semiconductor sample of cross-section A and length L is doped in such a way that the dopping concentration varies as $${N_D}left( x
ight) = {N_0}exp left( { - frac{x}{L}}
ight),,{N_0}$$ xa0 xa0 xa0is a constant. Assume that the mobility $$mu $$ of the majority carriers remains constant. The resistance R of the sample is given by

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?

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

The dielectric constant of water is 80. However its refractive index is 1.75 invalidating the expression n = ε 1/2 . This is because

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

In a cubic system with cell edge a, two phonons with wave vectors $${overrightarrow {x08f{q}} _1}$$ and $${overrightarrow {x08f{q}} _2}$$ collide and produce a third phonon with a wave. vector $${overrightarrow {x08f{q}} _3}$$ such that $${overrightarrow {x08f{q}} _1} + {overrightarrow {x08f{q}} _2} = {overrightarrow {x08f{q}} _3} + overrightarrow {x08f{R}} $$ xa0 xa0where, $$overrightarrow {x08f{R}} $$ is a lattice vector. Such a collision process will lead to
(a)

The thermal conductivity of a given material reduces, when it undergoes a transition from its normal state to the superconducting state. The reason is

Silicon has diamond structure with unit cell edge a = 0.542 nm. The interatomic separation is

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[{{
m{dot A}}}] . The volume of the primitive unit cell of the metal is

The dielectric constant of a material at optical frequencies is mainly due to

The temperature (T) dependence of magnetic susceptibility $$left( chi
ight)$$ of a ferromagnetic substance with Curie temperature (T c ) is given by

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

In an experiment involving a ferromagnetic medium, the following observations were made. Which one of the plots does not correctly represent the property of the medium?

For a three-dimensional crystal having N primitive unit cells with a basis of p atoms, the number of optical branches is

Which one of the following statements is not correct about the Brillouin Zones (BZ) of a square lattices with constant a?

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

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

Which one of the following statements about superconductors is not true?

Variation of electrical resistivity $$
ho $$ 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?

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?

In a one-dimensional Kronig-Penny model, the total number of possible wave functions is equal to

The plot of inverse magnetic susceptibility $$frac{1}{chi }$$ versus temperature T of an antiferromagnetic sample corresponds 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

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

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

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

For a conventional superconductor, which of the following statements is not true?

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

The order of magnitude of the energy gap of a typical superconductor is

The energy $$Eleft( {overrightarrow {x08f{k}} }
ight)$$ xa0of electrons of wave vector $$overrightarrow {x08f{k}} $$ in a solid is given by $$Eleft( {overrightarrow {x08f{k}} }
ight) = A{k^2} + B{k^4},$$ xa0 xa0where A and B are constants. The effective mass of the electron at $$left| {overrightarrow {x08f{k}} }
ight| = {k_0}$$ xa0is

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

Which one of the following statements is true?

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 $${omega ^2} = Cleft( {frac{{M + m}}{{Mm}}}
ight) pm {left[ {{C^2}{{left( {frac{{m + m}}{{Mm}}}
ight)}^2} - frac{{4{C^2}}}{{Mm}}{{sin }^2}frac{{ka}}{2}}
ight]^{frac{1}{2}}}$$ Which one of the following statements is incorrect?

The Hall coefficient R H of sodium depends on

Which one of the following axes of rotational symmetry is not permissible in single crystals?

The potential in a divalent solid at a particular temperature is represented by a one-dimensional periodic model. The solid should behave electrically as

The c/a ratio for an ideal hexagonal closed packed structure is

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

The critical magnetic field for a solid in superconducting state

The valence electrons do not directly determine the following property of a metal

The solid phase of an element follows van der Waals bonding with inter-atomic potential $$Vleft( r
ight) = - frac{P}{{{r^6}}} + frac{Q}{{{r^{12}}}}$$ xa0 xa0where, P and Q are constants. The bond length can be expressed as

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

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

If the ionic radii of Mn and S are 0.80 and 0.184 nm respectively, the structure of MnS will be

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 ?

Infrared absorption can be observed in which of the following molecules?

The number of independent elastic constants in an isotropic cubic solid is

The Bloch theorem states that within a crystal, the wave function $$psi left( {overrightarrow {x08f{r}} }
ight)$$ , of an electron has the form

In crystallographic notations, the vector $$overrightarrow {{x08f{OP}}} $$ xa0in the cubic cell shown in the figure is

The dependences of the magnetic susceptibility $$left( chi
ight)$$ of a material with temperature (T) can be represented by $$chi propto frac{1}{{T - heta }},$$ xa0 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?

In a crystal of N primitive cells, each cell contains two monovalent atoms. The highest occupied energy band of the crystal is

For a closed packed bcc structure of hard spheres, the lattice constant a is related to the sphere radius R as

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

Two dielectric materials A and B exhibit both ionic and orientational polarizabilities. The variation of their susceptibilities $$chi left( { = {varepsilon _r} - 1}
ight)$$ xa0 with temperature T is shown in the figure, where $${varepsilon _r}$$ is the relative dielectric constant. It can be inferred from the figure that

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

In an insulating solid which one of the following physical phenomena is consequence of Pauli's exclusion principle?

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

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

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]

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)

The primitive translation vectors of the body centred cubic lattice are $$overrightarrow {x08f{a}} = frac{a}{2}left( {{x08f{hat x}} + {x08f{hat y}} - {x08f{hat z}}}
ight),,overrightarrow {x08f{b}} = frac{a}{2}left( { - {x08f{hat x}} + {x08f{hat y}} + {x08f{hat z}}}
ight)$$ xa0 xa0 xa0 xa0and $$overrightarrow {x08f{c}} = frac{a}{2}left( {{x08f{hat x}} - {x08f{hat y}} + {x08f{hat z}}}
ight)$$ xa0 xa0. The primitive translation vectors $$overrightarrow {x08f{A}} ,,overrightarrow {x08f{B}} $$ xa0and $$overrightarrow {x08f{C}} $$ of the reciprocal lattice are