NEET Chemistry The Solid State Questions Solved

A metallic elements exists as a cubic lattice. Each edge of the unit cell is 2.88Å. The density of the metal is 7.20 g cm–3. How many unit cells will be present in 100 gm of the metal.

(1) 5.82 × 1023

(2) 6.33 × 1023

(3) 7.49 × 1024

(4) 6.9 × 1024

(1) The volume of unit cell (V) = a3 = (2.88Å)3 = $23.9×{10}^{-24\text{\hspace{0.17em}}}c{m}^{3}$

Volume of 100 g of the metal = $\frac{\text{Mass}}{\text{Density}}=\frac{100}{7.20}=13.9c{m}^{2}$

Number of unit cells in this volume = $\frac{13.9c{m}^{3}}{23.9×{10}^{-24}c{m}^{3}}=\text{\hspace{0.17em}}5.82×{10}^{23}$

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