Q.29 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.
Best answer
Answer: n = 4, face-centred cubic (fcc) lattice
\(\rho = \dfrac{nM}{a^3N_A}\ \Rightarrow\ n = \dfrac{\rho\,a^3N_A}{M}\)
\(a = 400\) pm \(= 4\times10^{-8}\) cm; \(a^3 = 64\times10^{-24} = 6.4\times10^{-23}\) cm\(^3\); \(\rho = 6.25\) g cm\(^{-3}\)
\(n = \dfrac{6.25 \times 6.4\times10^{-23} \times 6.022\times10^{23}}{60} = \dfrac{6.25 \times 38.54}{60} = \dfrac{240.9}{60} \approx 4\)
Four atoms per unit cell, so the lattice is face-centred cubic.
Nanoscience: Nanoscience is the study of phenomena and properties of materials at the nanoscale (about 1 nm to 100 nm), where the properties differ significantly from those of the bulk material.
Polyacrylonitrile: addition polymerisation of acrylonitrile (vinyl cyanide) in the presence of a peroxide catalyst:
n CH\(_2\)=CH–CN \(\xrightarrow{\text{peroxide}}\) –[CH\(_2\)–CH(CN)]\(_n\)– (polyacrylonitrile, Orlon/acrilan)
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