Solid State Physics MCQs Question and Answer in Engineering Physics

31

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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Answer & Solution

Answer: Option A

Solution:

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 T³. 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 T⁵ below the Debye temperature. The correct dependency below the Debye temperature is T³, not T⁵. Therefore, this option is not accurate.

32

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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Answer & Solution

Answer: Option C

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33

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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Answer & Solution

Answer: Option C

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34

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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Answer & Solution

Answer: Option D

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35

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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Answer & Solution

Answer: Option D

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36

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 T_c D) the plot of its susceptibility versus temperature is linear with an intercept T_c

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Answer & Solution

Answer: Option A

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37

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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Answer & Solution

Answer: Option C

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38

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_BT, which one of the following statements is true? (a and A are constants)

A) Dulong-Petit: $$C \propto \exp \left( {\frac{{ - a}}{T}} \right)$$ ; Einstein: C = constant; Debye: $$C \propto {\left( {\frac{T}{A}} \right)^3}$$ B) Dulong-Petit: C = constant; Einstein: $$C \propto {\left( {\frac{T}{A}} \right)^3}$$ ; Debye: $$C \propto \exp \left( {\frac{{ - a}}{T}} \right)$$ C) Dulong-Petit: C = constant; Einstein: $$C \propto \frac{{{e^{ - a/T}}}}{{{T^2}}}$$ ; Debye: $$C \propto {\left( {\frac{T}{A}} \right)^3}$$ D) Dulong-Petit: $$C \propto {\left( {\frac{T}{A}} \right)^3}$$ ; Einstein: $$C \propto \frac{{{e^{ - a/T}}}}{{{T^2}}}$$ ; Debye: C = constant

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Answer & Solution

Answer: Option C

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39

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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Answer & Solution

Answer: Option B

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40

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

A) $$\overrightarrow {\bf{A}} = \frac{{2\pi }}{a}\left( {{\bf{\hat x}} - {\bf{\hat y}}} \right);\,\overrightarrow {\bf{B}} = \frac{{2\pi }}{a}\left( {{\bf{\hat y}} + {\bf{\hat z}}} \right);\,\overrightarrow {\bf{C}} = \frac{{2\pi }}{a}\left( {{\bf{\hat x}} + {\bf{\hat z}}} \right)$$ B) $$\overrightarrow {\bf{A}} = \frac{{2\pi }}{a}\left( {{\bf{\hat x}} - {\bf{\hat y}}} \right);\,\overrightarrow {\bf{B}} = \frac{{2\pi }}{a}\left( {{\bf{\hat y}} - {\bf{\hat z}}} \right);\,\overrightarrow {\bf{C}} = \frac{{2\pi }}{a}\left( {{\bf{\hat x}} + {\bf{\hat z}}} \right)$$ C) $$\overrightarrow {\bf{A}} = \frac{{2\pi }}{a}\left( {{\bf{\hat x}} + {\bf{\hat y}}} \right);\,\overrightarrow {\bf{B}} = \frac{{2\pi }}{a}\left( {{\bf{\hat y}} + {\bf{\hat z}}} \right);\,\overrightarrow {\bf{C}} = \frac{{2\pi }}{a}\left( {{\bf{\hat x}} - {\bf{\hat z}}} \right)$$ D) $$\overrightarrow {\bf{A}} = \frac{{2\pi }}{a}\left( {{\bf{\hat x}} + {\bf{\hat y}}} \right);\,\overrightarrow {\bf{B}} = \frac{{2\pi }}{a}\left( {{\bf{\hat y}} + {\bf{\hat z}}} \right);\,\overrightarrow {\bf{C}} = \frac{{2\pi }}{a}\left( {{\bf{\hat x}} + {\bf{\hat z}}} \right)$$

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Answer & Solution

Answer: Option D

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