Q19 / 160 · TS EAMCET 2023 (12 May Shift 1) · Chemistry

At $\mathrm{T}(\mathrm{K})$, copper (atomic mass $=63.5 \mathrm{u}$ ) has fcc structure with an edge length of $\mathrm{x} Å$. The density of copper (in $\mathrm{g} \mathrm{cm}^{-3}$ ) at that temperature approximately is $\left(\mathrm{N}_{\mathrm{A}}=6.0 \times 10^{23} \mathrm{~mol}^{-1}\right)$

  • A
    $\frac{423}{x}$
  • B
    $\frac{4.23}{x^3}$
  • Correct answer
    C
    $\frac{423}{x^3}$
  • D
    $\frac{212.5}{x^3}$

Solution

$\begin{aligned} & \text { density (d) }=\frac{Z \times M}{N \times a} \\ & \text { for } \mathrm{Cu} ; \mathrm{z}=4(\text { for Fcc) } \\ & \mathrm{a}=\mathrm{x} Å=\mathrm{x} \times 10^{-8} \mathrm{~cm} \\ & \mathrm{~N}_{\mathrm{A}}=6.0 \times 10^{23} \mathrm{~mol}^{-1} \\ & \mathrm{M}=63.5 \mathrm{~g} \mathrm{mal}^{-1} \\ & \Rightarrow \mathrm{d}=\frac{(4)(63.5)}{\left(6.0 \times 10^{23}\right)\left(\mathrm{x} \times 10^{-8}\right)^3}=\frac{423.0}{\mathrm{x}^3}\end{aligned}$

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

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