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**Question 1: The arrangement of X^{â€“} ions around A^{+} ion in solid AX is given in the figure (not drawn to scale). If the radius of X^{â€“ }is 250 pm, the radius of A^{+} is (IIT JEE 2013)**

A

For octahedral Void

r

or

r

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 JEE-2012)****The empirical formula of the compound is****(a) MX****(b) MX _{2}**

X

Number of x

M

Number of M

Now: X: M = 4:2 = 2:1

So, the formula should be MX

Hence, the correct option is b.

**Question 3: The packing efficiency of the two-dimensional square unit cell shown below is (IIT JEE-2010)****(a) 39.27%****(b) 68.02%****(c) 74.05%****(d) 78.54%****Answer: d****Solution:**

Total number of the atoms per unit cell = Â¼(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/(2âˆš2 )

Or

Packing Efficiency = [(2Ã— Volume of one atom)/(Total volume of the unit cell)]Ã—100

=100 Ã— {2Ï€[L/(2âˆš2 )]^{2} }/L^{2}

= (Ï€/8 )Ã—100 = 78.54%

Hence, the correct option is D.

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