# Copper has FCC structures its atomic radius is 1.28 Å and atomic mass is 63.5 the density of copper will be

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Copper has FCC structures its atomic radius is 1.28 Å and atomic mass is 63.5 the density of copper will be
1. 8.9 × 103 kg/mm3
2. 8.9 × 103 kg/cm3
3. 8.9 × 103 kg/m3
4. 8.9 × 103 g/mm3

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Correct Answer - Option 3 : 8.9 × 103 kg/m3

Concept:

Theoretical density of a crystal structure:

$\rho = \frac{{nA}}{{{N_A}{V_c}}}$

N: Number of atoms associated with each unit cell

A: Atomic weight

Vc: Volume of unit cell

NA: Avogadro’s number (6.023 × 1023 atoms/mol)

Copper has FCC unit cell, thus:

n = 4

Vc = a3

In FCC:

$a = 2\sqrt 2 \;r$

Calculation:

Given, r = 1.28 Å = 1.28 × 10-10 m

$a = 2\sqrt 2 × 1.6 × {10^{ - 10}}$

Vc = a3

A = 63.5

${V_c} = {\left( {2\sqrt 2 × 1.28 × {{10}^{ - 10}}} \right)^3} = 4.74 × {10^{ - 29}}$ m3

$\rho = \frac{{nA}}{{{N_A}{V_c}}} = \frac{{4 × 63.5}}{{6.023 × {{10}^{23}} × 4.74 × {{10}^{ - 29}} × 1000}} = 8.89 × {10^3}\frac{{kg}}{{{m^3}}}\;$