MUNISH KAKAR’s INSTITUTE OF CHEMISTRY
BASIC CALCULATIONS IN SOLIDS WS#2
Q1.
Possible Types of Unit
Crystal Class
Axial Distances
Axial Angles
Cubic
a=b=c
α = β = γ = 90°
Tetragonal
a=b≠c
α = β = γ = 90°
Orthorhombic
a≠b≠c
α = β = γ = 90°
Hexagonal
a=b≠c
α = β = γ = 90°; γ = 120°
Primitive
Rhombohedral
a=b=c
α = β = γ = 90°
Primitive
Monoclinic
a≠b≠c
Triclinic
a≠b≠c
cells
Primitive, Body centred,
Face centred
Primitive, Body centred
Primitive, Body centred,
Face centred, End centred
α = β = γ = 90°;
Primitive and End centred
β ≠ 90°
α ≠ β ≠ γ ≠ 90°
Primitive
Which among the following is correct regarding Primitive cubic unit cell ?
(a) It has two atoms per unit cell and radius of atom is a
(b) It has one atoms per unit cell and radius of atom is a
2
2
3 a
4
a
(d) It has four atoms per unit cell and radius of atom is
2 2
(c) It has two atoms per unit cell and radius of atom is
Q2.
Which among the following is correct regarding Body centred cubic unit cell ?
(a) It has two atoms per unit cell and radius of atom is a
(b) It has one atoms per unit cell and radius of atom is a
2
2
3 a
4
a
(d) It has four atoms per unit cell and radius of atom is
2 2
(c) It has two atoms per unit cell and radius of atom is
Q3.
Which among the following is correct regarding face centred unit cell ?
(a) It has two atoms per unit cell and radius of atom is a
(b) It has one atoms per unit cell and radius of atom is a
2
2
3 a
4
a
(d) It has four atoms per unit cell and radius of atom is
2 2
(c) It has two atoms per unit cell and radius of atom is
Q4.
A metal crystallizes in fcc lattice and edge of the unit cell is 620 pm. The radius of metal
atom is
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(a) 265.5 pm
Q5.
M
g cm-3
x  N0
3
(c) Covalent crystal (d) Metallic crystal
(b)
M  N0
g cm-3
x3
(c)
4M
g cm-3
x  N0
3
(d)
M
g cm-3
4 x  N0
3
(b) 5.8 × 1023
(c) 2.9 × 1023
(d) 1.16 × 1024
A solid is made up of two elements A and B. Atoms of B are in FCC arrangement, while
atoms A occupy all edge centres . The formula of the compound is:
(a) AB2
Q9.
(b) Molecular crystal
A metallic element has simple cubic arrangement. The number of unit cells in 100 g of
this metal (edge length = 288 pm, density = 7.2 g cm-3) is 5.8 × 1023. The total number of
atoms in 100 gm of metal is:
(a) 2.32 × 1024
Q8.
(d) 438.6 pm
A metal has face centred cubic arrangement. If length of the edge of the cell is x pm and M
is its atomic mass, then density will be equal to (N0 is Avogadro number)
(a)
Q7.
(c) 310 pm
Which one has highest melting point?
(a) Ionic crystal
Q6.
(b) 219.2 pm
(b) AB
(c) AB3
(d) None of these
In a solid ‘AB’, ‘A’ atoms occupy the corners and face centres of the cubic unit cell and
atoms B occupy all edge centres and body centre positions of cube. If all the face-centred
atoms along one of the axes are removed, then the resultant stoichometry of the solid is
(a) AB2
(b) A2B
(c) A4B3
(d) A3B4
Q10. A compound formed by two elements X and Y crystallizes in the cubic structure where Y
atoms are at the corners of a cube and X atoms are at alternate faces. The formula of the
compound is:
(a) X2Y3
(b) XY3
(c) XY2
(d) X3Y2
XY
Q11. A compound formed by elements A and B has cubic structure in which A atoms are at the
corners of the cube and B atoms are at the face centres. The formula of the compound is:
(a) AB3
(b) A2B3
(c) A2B
(d) A4B3
Q12. The cell edge of a fcc crystal is 100 pm and its density is 10.0 g cm-3. The number of
atoms in 100 g of this crystal is:
(a) 1 × 1025
(b) 2 × 1025
(c) 3 × 1025
(d) 4 × 1025
Q13. A compound is formed by elements A and B. This crystallizes in the cubic structure where
the A atoms are at the corners of the cube and B atoms are at the body centres. The
simples formula of the compound is:
(a) AB
(b) A6B
(c) A8B4
(d) AB6
Q14. Explain why ionic compounds do not conduct electricity in solid state.
Q15. In an alloy of gold and cadmium if gold crystallizes in cubic structure occupying the
corners only and cadmium fits into edge centre voids, what is the formula of the alloy?
As Au atoms are at corners only
∴ No. of Au atoms = 8 × 1/8 = 1
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MUNISH KAKAR’s INSTITUTE OF CHEMISTRY
Q16.
Q17.
Q18.
Q19.
Q20.
Q21.
As Cd atoms are placed at edge centres. Hence,
No. of Cd atoms = 12 × ¼ = 3
As in unit cell no. of atoms of Au & Cd are in ratio 1 : 3
Au : Cd = 1 : 3
∴ Formula = AuCd3
If three elements X, Y and O crystallizes in a cubic solid lattice with X atoms at the
corners, Y atoms at cube centre and O atoms at edges then what is the formula of the
solid?
No. of X atoms = 8 × 1/8 = 1 (being at corner)
No. of Y atoms = 1 × 1 = 1 (being at body centre)
No. of O atoms = 12 × ¼ = 3 (being at edge centre)
∴ Formula of such solid = X : Y : O = 1 : 1 : 3
Hence XYO3
In NaCl crystal, Cl- ions have fcc arrangement. What is the number of Cl- ions per unit
cell?
4 atoms
A cubic solid is made of two elements X and Y. Atoms Y are at the corners of the cube and
X at the body centre. What is the formula of the compound?
No. of X atoms = 1 × 1 = 1
No. of Y atoms = 8 × 1/8 = 1
∴X:Y=1:1
What is the number of atoms in a unit cell of a face-centred cubic crystal?
In FCC arrangement, No. of atoms = 8 × 1/8 + 6 × ½ = 4
What type of interactions hold the molecules together in a polar molecular solid?
Dipole – Dipole attraction
What makes glass different from quartz? Under what conditions could quartz biconverted
into glass?
Glass = Amorphous solid
Quartz = Crystalline solid
(by extensive heating, Quartz can be changed to glass)
Below questions (22 – 35) will be discussed in Class on Saturday
Q22. An elements E crystallizes in body centred cubic structure. If the edge length of the cell is
1.469 × 10-10 m and the density is 19.3 g cm-3, calculate the atomic mass of this element.
Also calculate the radius of an atom of this element.
Q23. A compound contains two types of atoms-X and Y. It crystallizes in a cubic lattice with
atoms X at the corners of the unit cell and atoms Y at the body centres. What is the
simplest possible formula of this compound? What is the coordination of Y?
Q24. A compound formed by elements A and B has a cubic structure in which A atoms are at
the corners of the cube and B atoms are at the face centres. Derive the formula of the
compound.
Q25. If three elements, P, Q and R crystallize in a cubic solid lattice with P atoms at the
corners, Q atoms at the cube centre and R atoms at the centre of the faces of the cube,
then write the formula of the compound.
Q26. An element X with an atomic mass of 60 g mol-1 has density of 6.23 g cm-3. If the edge
length of its cubic unit cell is 400 pm, identify the type of cubic unit cell. Calculate the
radius of an atom of this element.
S.C.O. No. 203, SECOND FLOOR, SECTOR 14, PANCHKULA. Phone : 9417655033, 9888019721
MUNISH KAKAR’s INSTITUTE OF CHEMISTRY
Q27. Silver forms FCC lattice and X-ray studies of its crystals show that the edge length of its
unit cell is 408.6 pm. Calculate the density of silver (Atomic mass = 107.9 u).
Q28. Analysis shows that a metal oxide has the empirical formula M 0.96 O1.00. Calculate the
percentage of M2+ and M3+ ions in this crystal?
Q29. Silver crystallizes with face-centred cubic unit cells. Each side of the unit cell has a length
of 409 pm. What is the radius of an atom of silver? (Assume that each face atom is
touching the four corner atoms.)
Q30. The density of copper metal is 8.95 g cm-3. If the edge length of the unit cell is 361.5 pm,
is the copper unit cell simple cubic, body centred cubic or face centred cubic?
(Given: Atomic mass of Cu = 63.54 g mol-1 and NA = 6.02 × 1023 mol-1).
Q31. Silver crystallizes in face-centred cubic unit cell. Each side of this unit cell has a length of
400 pm. Calculate the radius of the silver atom. (Assume the atoms just touch each other
on the diagonal across the face of the unit cell, that is each face atom is touching the four
corner atoms.)
Q32. The density of lead is 11.35 g cm-3 and the metal crystallizes with fcc unit cell. Estimate
the radius of lead atom. (At. mass of lead = 207 g mol-1 and NA = 6.02 × 1023 mol-1)
Q33. Silver crystallizes in face centred cubic (fcc) unit cell. If the radius of silver atom is 145
pm, what is the length of each side of the unit cell?
Q34. Tungsten crystallizes in body centred cubic unit cell. If the edge of the unit cell is 316.5
pm, what is the radius of tungsten atom?
Q35. Copper crystallizes with face centred cubic unit cell. If the radius of copper atom is 127.8
pm. Calculate the density of copper metal. (Atomic mass of Cu = 63.55 u and Avogadro’s
number NA = 6.02 × 1023 mol-1)
S.C.O. No. 203, SECOND FLOOR, SECTOR 14, PANCHKULA. Phone : 9417655033, 9888019721