1.

A substance AB crystallizes in cubic closest missing then calculate fraction of body diagonal
packing (C.C.P.) with B occupying half the covered by species in the defective crystal.
tetrahedral voids. One litre of the crystal is
doped with 1 mole atoms of C some of which 7. A non stoichiometric compound Fe7Sg consist
replace the B atoms and remaining occupy few of iron in both Fe+2 and Fe+3 form and sulphur
interstitial voids without affecting the is present as sulphide ions. Calculate cation
dimensions of cubic crystal lattice. If density of vacancies as a percentage of Fe+2 initially
crystal before doping is 4.8 gm/milliliter and present in the sample.
density after doping is 4.795 gm /ml, then 100
[Express your answer as % and you should
calculate % of C added which replace B atoms. x
(Given : Atomic weight : A, B and C : 40, 30, write x as answer]
15)
8. Calculate radius of an atom (in Å) the crystal
2. The density of solid argon is 1.6 gm/ml at - 3.2 π
233C. If the atomic volume of argon is assumed which has a density equal to gm/ml and
3
5 −23 the edge length of the cubic unit cell is 5 Å if
to be ×10 , then what % of solid argon is
3 atomic mass of the metal is 40 T. [
apparently empty space? 23
Take : N A =6 ×10 ]
[Express your answer by dividing with 15]
9. A metal M has an atomic mass of 60. If atomic
3. A metal A exists in the bcc structure having radius of metal is 7.53Å and density of metal =
uncovered length between the atoms along the
1
edge. equal to 1.2 Å. If molar mass of the metal gm/ml, then what will be the edge length of
135
is 307.2 gm/mole, then calculate density of the
the cubic crystal unit cell obtained using metal
crystal in gm/ml. [Use :
M?
N A =6 ×10 ∧√3=1.7]
23
23
Express answer in nm. [N A=6× 10 ]

4. Calculate packing fraction of CsCl structure. ¿

10. An ionic compound ( A ¿ ) crystallizes in rock
22
Use: √ 3=1.732 , π= . Assume no distortion +¿ ¿
salt structure, If the ionic radii of A and B
−¿ ¿
7
is 200 pm and 400 pm respectively, then
in the crystal. Express your answer after
calculate distance between nearest cations in Å.
multiplying your answer with 1050 ∴ If your
1
answer is you should write 1000. 11. The difference in coordination numbers of
1.05
hexagonal close packing in 3D and square close
packing in 2-D, of identical spheres is :
5. Calculate packing fraction of hexagonal packing
of circles in two dimension.
12. Calculate the packing efficiency of a FCC

[ Given :
π
3 √3 ]
=0.600 Express your answer crystal in which all the tetrahedral and
octahedral voids are occupied by the largest
after multiplying your answer with 1000. spheres without disturbing the lattice.

6. An ideal ionic crystal is having rock salt 13. The C.N.of the barium ion Ba2+¿¿ in BaF 2 is 8.
−¿ ¿ +¿ ¿
structure (A+ B ) such that A is occupying −¿¿
What must be the C.N. of F ion?
octahedral void. The crystal is doped with atoms
of C which occupy all the tetrahedral voids 14. Calculate the edge length of the unit cell of
without distorting the lattice. If the crystal shows sodium chloride given density of NaCl is
defect such that the body centered atom is 3 −3
2.17 x 10 k gm and molecular weight
−3 −1
58.5 ×10 kg mol .
 molecules are contained in a unit cell? (Density
2 of ice = 0.92 gm/cc)
15. The density of solid argon is
3
( amu/¿ Å3 ) at
40K. If the Argon atom is assumed to be sphere
3
to radius 1/3 À, what percentage of solid
π
Argon is apparently without anything?
16. A mineral of iron contains an oxide containing 22. In the sodium chloride structure, each Na ion
+¿¿

72.36% iron by mass and has a density of 5.2 is

g/cc. Its unit cell is cubic with edge length of −¿¿
surrounded by six Cl ions nearest neighbours
839 pm. What is the total number of atoms +¿¿
and …… Na ions next nearest neighbours.
(ions) present in each unit cell?
23. Please help Sabu decode the jail lock. Chacha
17. An ionic solid AB2 isomorphous to the rutile
Choudhary gave Sabu a formula :
structure (a tetragonal system with effective
number of formula units = 2) has edge lengths of
the unit cell of 4 Å, 4 Å and 7 Å. Calculate the
f 1= ( xz × y) ; f =( vt ×u); f =( rs × w )
2 3

density of the substance if its formula weight is Sabu can open the lock if he finds the value of
3 f 1+ f 2 +f 3=¿ key where :
80. Take N A =¿ 6 ×10 23 and express your
answer in mg/cc using four significant digits. Number of triangular faces in a truncated
tetrahedron = x
18. Consider the arrangement of circles of equal Number of hexagonal faces in a truncated
radii with centers arranged as per the 2- tetrahedron = y
Number of corners in a truncated tetrahedron = z
dimensional lattice defined by a = b, θ=60 °
Number of square faces in a truncated
such that each circle is touching all its nearest
octahedron =t
neighbours. If all the void areas present are
Number of hexagonal faces in a truncated
additionally occupied by smaller circles of
octahedron = u
relevant size so that the void circles are just
Number of corners in a truncated octahedron = v
contacting their neighbours find the packing
Number of triangular faces in a truncated cube =
efficiency of the configuration in percent.
w
Number of octagonal faces in a truncated cube =
19. In a solid r ¿ ¿= 1.6 Å and r ¿ ¿= 1.864 Å. Use the
r
radius ratio rule to determine the edge length of
Number of corners in a truncated cube = s
the cubic unit cell in Å.
What is the KEY?

20. There are 5.6 ×10 24 unit cells in 1 kg of metal

24. Argon crystallizes in FCC arrangement and
for which the density is 7.5 g/cc. Calculate the density of solid and liquid argon is 3.7 and 3
side length of the cubic unit cell of the lattice of gm/cc respectively. Find percentage of empty

( )
1 /3
100 space in liquid Ar.
the metal. (Use =2.877) Express your
42
answer in Å, by applying appropriate 25. In a FCC unit cell of A atom (At wt. = 150)
approximation. having side length 10A. Number of atom per
unit cell is Z, number, of next nearest neighbour
21. Ice crystallizes in a hexagonal lattice. At the low is X and packing All the three interfacial angles
temperature at which the structure determined, and all the three efficiency is y % find value of
the lattice constants were a = 4.53 Å was and c = yz
7.41 Å (as shown in fig). How many H 2 O ( x +1 )
2
26. If number of nearest neighbours, next nearest
(2nd nearest) neighbour and next to next nearest
(3rd nearest) neighbours are x, y and z
respectively for body centered cubic unit cell,
xy
then calculate value of
z

27. Number of crystal systems having, only 2 types

of Bravais lattices = x, Number of crystal
systems having, at least 2 interfacial angles
equal = y, All the three interfacial angles and all
the three axes lengths equal = z. Then find y -(x
+z).

28. If packing fraction of two dimension unit cell

shown in figure is A, then calculate value of
1000 A. [Take π=3.2, √ 2=1.4 ]
Fill your answer as sum of digits (excluding
decimal places) till you get the single digit
answer.

ANSWER KEY: