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Question

# The edge length of unit cell of a metal having molecular weight 75 g/mol is 5 ˚A which crystallises in cubic lattice. If the density is 2 g/cc then find the radius of a metal atom. (NA=6×1023 ). Give the answer in pm.

A
217pm
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B
210pm
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C
220pm
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D
205pm
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Solution

## The correct option is A 217pmTheoretical density of crystal is given by ρ=nMNoa3 g/cm3 ⇒n=ρN0Ma3 ⇒n=2×6.022×1023×(5)3×(10−8)375=2 So, it is body centered cubic (BCC) structure. For BCC, if a is the edge length of the cube and r is the radius of the atom then, 4r=√3a ⇒r=√34a =√34×5 ˚A ⇒r=2.165 ˚A=2.165×10−8 cm=216 pm

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