Q22 / 160 · WBJEE 2015 · Chemistry

Suppose the mass of a single Ag-atom is $m$. Ag metal crystallises in fcc lattice with unit cell of length $a$. The density of Ag metal in terms of $a$ and $m$ is

  • Correct answer
    A
    $\frac{4 m}{a^{3}}$
  • B
    $\frac{2 m}{a^{3}}$
  • C
    $\frac{m}{a^{3}}$
  • D
    $\frac{m}{4 a^{3}}$

Solution

Given that, Mass of single Ag-atom $=m$ Unit cell length $=a$ Total atoms present per unit cell of fcc lattice $=4$ Therefore, mass of unit cell becomes $4 \mathrm{m}$. Volume of unit cell $=a^{3}$ Density $(\rho)=\frac{\text { Mass of unit cell }}{\text { Volume of unit cell }}=\frac{4 \mathrm{m}}{\mathrm{a}^{3}}$

Hence, the correct answer is option: 'A'.

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