At 100℃, copper (Cu) has FCC unit cell structure with cell edge length of x Å. What is the approximate density of Cu (in g m^{-3}) at this temperature?

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JEE Mains Previous Paper 1 (Held On: 9 Jan 2019 Shift 2)

Option 4 : \({\rm{\;}}\frac{{422}}{{{x^3}}}\)

JEE Mains Previous Paper 1 (Held On: 12 Apr 2019 Shift 2)

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**Calculation:**

For Fcc, the rank of the unit cell (Z) = 4

Mass of one Cu-atom, M - 63.55 u

Avogadro’s number, N_{A} = 6.023 × 10^{23} atom

Edge length, \(a\) = x Å = x × 10^{-8}cm

Density, \(\left( {\rm{d}} \right) = {\rm{\;}}\frac{{Z \times M}}{{{N_A} \times {a^3}}}\)

\(= \frac{{4 \times 63.55}}{{6.023 \times {{10}^{23}} \times {{\left( {x \times {{10}^{ - 8}}} \right)}^3}}}\)

\(= \frac{{422.048}}{{{x^3}}}\;g\;c{m^{ - 3}}\)