Question 1: The arrangement of X^{–} ions around A^{+} ion in solid AX is given in the figure (not drawn to scale). If the radius of X^{– }is 250 pm, the radius of A^{+} is (IIT JEE 2013)
(a) 104 pm
(b) 125 pm
(c) 183 pm
(d) 57 pm
Answer: a
Solution:
A^{+} is present in the octahedral void of X^{}.
For octahedral Void
r^{+}/r^{} = 0.414
or
r^{+} = 0.414 r^{} = 0.414 × 250 pm ≈104 pm
Hence, the correct option is a.
Question 2: A compound MpXq has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below. (IIT JEE2012)
The empirical formula of the compound is
(a) MX
(b) MX_{2}
(c) M_{2}X
(d) M_{5}X_{14}
Answer: b
Solution:
X^{} ions are present at the corners and face centers:
Number of x^{} ions per lattice = 1/8 (Number of ions present at corners of cube) + ½ (Number of ions present at face centers) = 1/8(8) + ½(6) = 4
M^{+} ions are present at the four edge centers and at body center. corners and on face centers:
Number of M^{+} ions per lattice = 1/4(Number of ions present at edge centers of cube) + (Number of ions present at body center) = 1/4(4) + 1 = 2
Now: X: M = 4:2 = 2:1
So, the formula should be MX_{2}
Hence, the correct option is b.
Question 3: The packing efficiency of the twodimensional square unit cell shown below is (IIT JEE2010)
(a) 39.27%
(b) 68.02%
(c) 74.05%
(d) 78.54%
Answer: d
Solution:
Total number of the atoms per unit cell = ¼(4) +1 = 2
Let, Radious of the atom = r
SR = QR =PQ = SP =L
&
QS = 4r
Now, in triangle SRP,
SR^{2 }+ QR^{2} =SQ^{2}
Or
L^{2}+L^{2} =(4r)2
r = L/(2√2 )
Or
Packing Efficiency = [(2× Volume of one atom)/(Total volume of the unit cell)]×100
=100 × {2π[L/(2√2 )]^{2} }/L^{2}
= (π/8 )×100 = 78.54%
Hence, the correct option is D.
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