Predict the type of cubic lattice of a solid element having edge length of 400 pm and density is 6.25 g/ml (At

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Q. Predict the type of cubic lattice of a solid element having edge length of 400 pm and density is 6.25 g/ml (Atomic mass of element = 60). Define: Nanoscience. Write chemical reaction for the preparation of polyacrylonitrile.

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$Z=\rho a^3N_A/M\approx4$ → FCC lattice. Nanoscience studies 1–100 nm structures. Polyacrylonitrile from acrylonitrile via addition polymerisation.

Given: edge length $a = 400\ pm = 4\times10^{-8}\ cm$ , density $\rho = 6.25\ g/mL$ , atomic mass $M=60\ g/mol$ .

Using $\rho = \dfrac{ZM}{a^3N_A}$ :

$Z = \dfrac{\rho\,a^3\,N_A}{M} = \dfrac{6.25 \times (4\times10^{-8})^3 \times 6.022\times10^{23}}{60}$

$a^3 = 64\times10^{-24}\ cm^3$

$Z = \dfrac{6.25 \times 64\times10^{-24} \times 6.022\times10^{23}}{60} = \dfrac{6.25\times64\times6.022}{60} \approx 4.01 \approx 4$

$Z=4$ corresponds to a face-centred cubic (FCC) lattice.

Nanoscience: the branch of science dealing with the study, synthesis, and properties of materials and structures whose dimensions lie in the nanometre range (about 1–100 nm), where properties differ significantly from the bulk.

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In a body-centred cubic lattice, atoms touch along the body diagonal, giving $4r=\sqrt3\,a$ , i.e. $r=(\sqrt3/4)a$ .

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Q.Predict the type of cubic lattice of a solid element having edge length of 400 pm and density is 6.25 g/ml (Atomic mass of element = 60). Define: Nanoscience. Write chemical reaction for the preparation of polyacrylonitrile.

Concept understanding — Crystal Lattices and Unit Cells

Q.Predict the type of cubic lattice of a solid element having edge length of 400 pm and density is 6.25 g/ml (Atomic mass of element = 60). Define: Nanoscience. Write chemical reaction for the preparation of polyacrylonitrile.

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