When gold crystallizes, it forms face-centered cubic cells. The unit cell edge length is 4 × 10–8 cm. Calculate the density of gold. Molar mass of gold is 197 g mol–1.

Q.3 When gold crystallizes, it forms face-centered cubic cells. The unit cell edge length is 4 × 10^–8 cm. Calculate the density of gold. Molar mass of gold is 197 g mol^–1.

Doubtly Asked 28 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

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Answer: Density of gold ≈ 20.45 g cm^–3

Given: fcc, so \(n = 4\); \(a = 4\times10^{-8}\) cm; \(M = 197\) g mol^–1; \(N_A = 6.022\times10^{23}\) mol^–1.

\(a^3 = (4\times10^{-8})^3 = 64\times10^{-24}\ \text{cm}^3\)

\(\rho = \dfrac{nM}{a^3 N_A} = \dfrac{4\times197}{64\times10^{-24}\times6.022\times10^{23}} = \dfrac{788}{38.54} = 20.45\ \text{g cm}^{-3}\)

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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When gold crystallizes, it forms face-centered cubic cells. The unit cell edge length is 4 × 10–8 cm. Calculate the density of gold. Molar mass of gold is 197 g mol–1.

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