Solid State Chemistry Questions and Answers

Q: A dislocation with Burgers vector that equals one lattice spacing is called ............................. dislocation.

Such a dislocation is called a unit dislocation.A unit (perfect) dislocation has a Burgers vector equal to one full lattice translation, so the crystal on either side of the slipped region is perfectly matched and no stacking fault is left behind.A partial (imperfect) dislocation has a Burgers vector that is only a fraction of a lattice vector and bounds a stacking fault. A Frank partial is one such case, with its Burgers vector perpendicular to the slip plane.

Q: According to Debye theory, specific heat at high temperature is proportional to :

At high temperature the specific heat is independent of T.Debye theory treats a solid's vibrations as phonons up to a cut-off frequency. Well above the Debye temperature every mode is fully excited, each contributing kT, so the molar heat capacity levels off at 3R, about 25 J/(mol K). That is the Dulong-Petit law, which the theory reproduces.The T3 dependence is the Debye law at low temperature, the trap here. A linear T term is the electronic contribution in metals at low temperature, and T2 does not apply to three-dimensional solids.

Q: A compound contains two types of atoms X and Y. It crystallizes in a cubic lattice with atom X at the corners of the unit cell and Y at the body centre. The simplest possible formula of this compound is :

The formula is XY.An atom at a corner of a cubic unit cell is shared by eight cells, and an atom at the body centre belongs wholly to one cell:\[ \begin{aligned} \mathrm{X} &= 8 \times \tfrac{1}{8} = 1 \\ \mathrm{Y} &= 1 \times 1 = 1 \end{aligned} \]One X and one Y per cell gives XY, the arrangement of the cesium chloride structure.X2Y and X4Y come from counting corner atoms as more than one-eighth each, and XY4 reverses the roles of the two atoms. The same counting with face centres (each shared by two cells) is what gives XY3 in a face-centred arrangement.

Q: A compound formed by element X and Y crystallizes in cubic structure in which atoms of ‘X’ are at the corners while that of ‘Y’ are at the face centre. The formula of the compound is :

The formula is XY3.Count the atoms belonging to one unit cell. A corner atom is shared by eight cells and a face-centre atom by two:\[ \begin{aligned} \mathrm{X} &= 8 \times \tfrac{1}{8} = 1 \\ \mathrm{Y} &= 6 \times \tfrac{1}{2} = 3 \end{aligned} \]One X to three Y gives XY3, as in the Cu3Au type of ordered alloy.X8Y6 counts the positions without sharing them among neighbouring cells. X3Y and 3XY reverse or misplace the factor of three, which belongs to the face-centred Y atoms.

11.

A dislocation with Burgers vector that equals one lattice spacing is called ............................. dislocation.

A.Unit
B.Partial
C.Imperfect
D.Frank

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: A

Such a dislocation is called a unit dislocation.

A unit (perfect) dislocation has a Burgers vector equal to one full lattice translation, so the crystal on either side of the slipped region is perfectly matched and no stacking fault is left behind.

A partial (imperfect) dislocation has a Burgers vector that is only a fraction of a lattice vector and bounds a stacking fault. A Frank partial is one such case, with its Burgers vector perpendicular to the slip plane.

Discuss in Forum

12.

According to Debye theory, specific heat at high temperature is proportional to :

A.T
B.\(\mathrm{T^{2}}\)
C.\(\mathrm{T^{3}}\)
D.Independent of T

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: D

At high temperature the specific heat is independent of T.

Debye theory treats a solid's vibrations as phonons up to a cut-off frequency. Well above the Debye temperature every mode is fully excited, each contributing kT, so the molar heat capacity levels off at 3R, about 25 J/(mol K). That is the Dulong-Petit law, which the theory reproduces.

The T³ dependence is the Debye law at low temperature, the trap here. A linear T term is the electronic contribution in metals at low temperature, and T² does not apply to three-dimensional solids.

Discuss in Forum

13.

A compound contains two types of atoms X and Y. It crystallizes in a cubic lattice with atom X at the corners of the unit cell and Y at the body centre. The simplest possible formula of this compound is :

A.\(\mathrm{X_{2}Y}\)
B.\(\mathrm{X_{4}Y}\)
C.XY
D.\(\mathrm{XY_{4}}\)

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: C

The formula is XY.

An atom at a corner of a cubic unit cell is shared by eight cells, and an atom at the body centre belongs wholly to one cell:

\[ \begin{aligned} \mathrm{X} &= 8 \times \tfrac{1}{8} = 1 \\ \mathrm{Y} &= 1 \times 1 = 1 \end{aligned} \]

One X and one Y per cell gives XY, the arrangement of the cesium chloride structure.

X₂Y and X₄Y come from counting corner atoms as more than one-eighth each, and XY₄ reverses the roles of the two atoms. The same counting with face centres (each shared by two cells) is what gives XY₃ in a face-centred arrangement.

Discuss in Forum

14.

A compound formed by element X and Y crystallizes in cubic structure in which atoms of ‘X’ are at the corners while that of ‘Y’ are at the face centre. The formula of the compound is :

A.3XY
B.\(\mathrm{X_{3}Y}\)
C.\(\mathrm{XY_{3}}\)
D.\(\mathrm{X_{8}Y_{6}}\)

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: C

The formula is XY₃.

Count the atoms belonging to one unit cell. A corner atom is shared by eight cells and a face-centre atom by two:

\[ \begin{aligned} \mathrm{X} &= 8 \times \tfrac{1}{8} = 1 \\ \mathrm{Y} &= 6 \times \tfrac{1}{2} = 3 \end{aligned} \]

One X to three Y gives XY₃, as in the Cu₃Au type of ordered alloy.

X₈Y₆ counts the positions without sharing them among neighbouring cells. X₃Y and 3XY reverse or misplace the factor of three, which belongs to the face-centred Y atoms.

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