Question

At ${100}^{\circ }C,$ copper $\left(Cu\right)$ has fcc unit cell structure with cell edge length of $x\stackrel{\circ }{A}$ . what is the approximate density of Cu $\left(\text{in g}c{m}^{-3}\right)$ at this temperature? [Atomic mass of $Cu$ $=63.55u]$
(JEE Main 2019)

• A. $\frac{211}{x^3}$
• B. $\frac{105}{x^3}$
• C. $\frac{422}{x^3}$
• D. $\frac{205}{x^3}$

Answer 1

The correct option is C $\frac{422}{x^3}$

Copper $\left(Cu\right)$ has fcc unit cell structure, therefore, Z = 4 $density,d=\frac{4\times M}{N_A(a{)}^3}$ $d=\frac{63.5\times 4}{6\times {10}^{23}\times x^3\times {10}^{-24}}g/c{m}^3$ $d=\frac{63.5\times 4\times 10}{6\times x^3}g/c{m}^3$ $d=\frac{423.33}{x^3}=\left(\frac{422}{x^3}\right)$