Question

A metallic element has a cubic lattice. Each edge of the unit cell is $2\stackrel{\circ }{A}$. the density of the metal is $2.5gc{m}^{-3}$. The unit cells in $200g$ of metal are:

• A. $1\times {10}^{24}$
• B. $1\times {10}^{20}$
• C. $1\times {10}^{22}$
• D. $1\times {10}^{25}$

Answer 1

The correct option is D $1\times {10}^{25}$

Number of unit cells $=\frac{\text{mass of metal}}{\text{mass of one unit cell}}$

Given, edge length of unit cell

$=2\stackrel{\circ }{A}=2\times {10}^{-8}cm$

Mass of metal $=200g$

Density of metal $=2.5gc{m}^{-3}$

Volume of unit cell

$=(edgelength{)}^3=(2\times {10}^{-8}{)}^3$

$=8\times {10}^{-24}c{m}^3$

Mass of one unit cell $=volume\times density$

$=8\times {10}^{-24}\times 2.5$

$=20\times {10}^{-24}$

$\therefore$ No. of unit cells in $200g$ metal

$=\frac{\text{mass of metal}}{\text{mass of one unit cell}}$

$=\frac{200}{20\times {10}^{-24}}$

$=10\times {10}^{24}=1.0\times {10}^{25}$