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Question

# A solid element exists in simple cubic crystal. If its atomic radius is 1.0 oA and the ratio of packing fraction to density is 0.1 cm3/g, then the atomic mass of the element is (NA≈6×1023)

A
8π
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B
16π
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C
6π
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D
4π
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Solution

## The correct option is A 8πGiven element exist in simple cubic crystal ∴ Zeff=1 Atomic radius, r=1.0 oA=10−8 cm For sc, Packing fraction =Z×Volume occupied by sphereVolume of the cube Packing Fraction, P.F. =Z×43πr3a3 Density, ρ=Z×Ma3×NA where, a is edge length of unit cell. Ratio of P.F.ρ=4πr3×NA3×M=0.1 ⇒4π×(10−8)3×6×10233×M=0.1 M=8π

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