The edge length of unit cell of a metal having molar mass 75 g mol−1 is 5˚A which crystallizes in body centered cubic lattice. If density is 2 g cm−3, calculate the radius (in pm) of metal atom.
A
216
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B
214
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C
100
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D
2.14
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Solution
The correct option is B216
The expression for density is as follows:
Density=n×Molar massV×Na 2=2×75a3×6.023×1023 (n=2 for bcc) ∴a=5×10−8 cm3 ∵r=√34×a=√34×5×10−8=2.16×10−8 cm =216 pm