Solid StateHard
Question
A solid element (monoatomic) exists in cubic crystal. If its atomic radius is 1.0 Å and the ratio of packing fraction and density is 0.1 cm3/g, then the atomic mass of the element is (NA = 6 × 1023)
Options
A.8π
B.16π
C.80π
D.4π
Solution
$\frac{P.F.}{d} = \frac{V_{\text{Particle}}/V_{\text{Unitcell}}}{m_{\text{Particle}}/V_{\text{unitcell}}} = \frac{V_{\text{Particle}}}{m_{\text{Particle}}}$
Or, $0.1 = \frac{Z \times \frac{4}{3}\pi\left( 1.0 \times 10^{- 8} \right)^{3}}{Z \times M/6 \times 10^{23}} \Rightarrow M = 8\pi$
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