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?
A. EA > EB
B. EA < EB
C. EA = EB
D. EA and EB both depend on temperature
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In a one-dimensional Kronig-Penny model, the total number of possible wave functions is equal to
A. twice the number of unit cells
B. number of unit cells
C. half the number of unit cells
D. independent of the number of unit cells
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The plot of inverse magnetic susceptibility χ 1
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An n-type semiconductor has an electron concentration of 3 × 1020 m-3 . If the electron drift velocity is 100 m/s in an electric field of 200 V/m, the conductivity (in Ω − 1 -1 ) of this material is
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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
A. 1 0 0
B. 1 1 0
C. 1 1 1
D. 2 0 0
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An intrinsic semiconductor with mass of a hole mh , and mass of an electron me is at a finite temperature T. If the top of the valence band energy is Ev and the bottom of the conduction band energy is Ec , the Fermi energy of the semiconductor is
A. E F = ( 2 E v + E c ) − 4 3 k B T ln ( m e m h )
B. E F = ( 2 k B T ) + 4 3 ( E v + E c ) ln ( m e m h )
C. E F = ( 2 E v + E c ) + 4 3 k B T ln ( m e m h )
D. E F = ( 2 k B T ) − 4 3 ( E v + E c ) ln ( m e m h )
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A superconducting ring is cooled in the presence of a magnetic field below its critical temperature (Tc ). The total magnetic flux that passes through the ring is
A. zero
B. n 2 e h
C. 4 π e nh
D. h c n e 2
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For a conventional superconductor, which of the following statements is not true?
A. Specific heat is discontinuous at transition temperature Tc
B. The resistivity falls sharply at Tc
C. It is diamagnetic below Tc
D. It is paramagnetic below Tc
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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
A. (2, 1, 2)
B. (1, 1, 1)
C. (2, 0, 0)
D. (3, 1, 1)
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The order of magnitude of the energy gap of a typical superconductor is
A. 1 MeV
B. 1 keV
C. 1 eV
D. 1 meV
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In simple metals the phonon contribution to the electrical resistivity at temperature T is
A. directly proportional to T above Debye temperature and to T3 below it
B. inversely proportional to T for all temperatures
C. independent of T for all temperatures
D. directly proportional to T above Debye temperature and to T5 below it
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The effective mass of an electron in a semiconductor
A. can never be positive
B. can never be negative
C. can be positive or negative
D. depends on its spin
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Which one of the following is not correct statement about semiconductors?
A. The electrons and holes have different mobilities in a semiconductor
B. In an n-type semiconductor, the Fermi level lies closer to the conduction band edge
C. Silicon is a direct band gap semiconductor
D. Silicon has diamond structure
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The effective mass of an electron in a semiconductor can be
A. negative near the bottom of the band
B. a scalar quantity with a small magnitude
C. zero at the centre of the band
D. negative near the top of the band
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A solid superconductor is placed in an external magnetic field and then cooled below its critical temperature. The superconductor
A. retains its magnetic flux because the surface current supports it
B. expels out its magnetic flux because it behaves like a paramagnetic material
C. expels out its magnetic flux because it behaves like an antiferromagnetic material
D. expels out its magnetic flux because the surface current induces a field in the direction opposite to the applied magnetic field
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A ferromagnetic material has a Curie temperature 100 K. Then,
A. its susceptibility is doubled when it is cooled from 300 K to 200 K
B. all the atomic magnets in it get oriented in the same direction above 100 K
C. the plot of inverse susceptibility versus temperature is linear with a slope Tc
D. the plot of its susceptibility versus temperature is linear with an intercept Tc
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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. the slope of E versus k is proportional to the group velocity
B. the slope of E versus k has its maximum value at |k| = π/a
C. the plot of E versus k will be parabolic in the interval (-π/a) < k < (π/a)
D. the slope of E versus k is non-zero for all k the interval (-π/a) < k(π/a)
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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 ≫ kB T, which one of the following statements is true? (a and A are constants)
A. Dulong-Petit: C ∝ exp ( T − a ) C ∝ ( A T ) 3
B. Dulong-Petit: C = constant; Einstein: C ∝ ( A T ) 3 C ∝ exp ( T − a )
C. Dulong-Petit: C = constant; Einstein: C ∝ T 2 e − a / T C ∝ ( A T ) 3
D. Dulong-Petit: C ∝ ( A T ) 3 C ∝ T 2 e − a / T
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A cubic cell consists of two atoms of masses m, and m2 (m1 > m2 ) with m1 and m2 atoms situated on alternate planes. Assuming only nearest neighbour interactions, the centre of mass of the two atoms
A. moves with the atoms in the optical mode and remains fixed in the acoustic mode
B. remains fixed in the optical mode and moves with the atoms in the acoustic mode
C. remains fixed in both optical and acoustic modes
D. moves with the atoms in both optical and acoustic modes
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The primitive translation vectors of the body centred cubic lattice are
a = 2 a ( x ^ + y ^ − z ^ ) , b = 2 a ( − x ^ + y ^ + z ^ ) and
c = 2 a ( x ^ − y ^ + z ^ ) . The primitive translation vectors
A , B and
C of the reciprocal lattice are
A. A = a 2 π ( x ^ − y ^ ) ; B = a 2 π ( y ^ + z ^ ) ; C = a 2 π ( x ^ + z ^ ) B. A = a 2 π ( x ^ − y ^ ) ; B = a 2 π ( y ^ − z ^ ) ; C = a 2 π ( x ^ + z ^ ) C. A = a 2 π ( x ^ + y ^ ) ; B = a 2 π ( y ^ + z ^ ) ; C = a 2 π ( x ^ − z ^ ) D. A = a 2 π ( x ^ + y ^ ) ; B = a 2 π ( y ^ + z ^ ) ; C = a 2 π ( x ^ + z ^ ) Select an option to see the answer and solution.
