Q22 / 160 · TS EAMCET 2020 (10 Sep Shift 1) · Chemistry

Copper crystallises in cсp arrangement and accepted value of metal ion radius was found to be $1.14 Å$. Calculate the density of copper in grams per cubic centimetre. (Atomic weight of copper is $64, N_A=6 \times 10^{23}$ )

  • Correct answer
    A
    6.67
  • B
    7.80
  • C
    8.90
  • D
    10.00

Solution

Given, copper crystallises in ccp manner radius $=1.41 Å=141 \mathrm{pm}$ Atomic weight of copper $=64$ Avogadro's number $=6 \times 10^{23}$, Density $=$ ? $\rho=\frac{Z \times M}{a^3 \times N_a}$ Here, edge length of unit cell can be calculate as $\begin{aligned} & r=\frac{a}{2 \sqrt{2}} \Rightarrow a=r \times 2 \sqrt{2} \\ & a=141 \times 2 \times 1.414 \\ & a=398.74 \text { pm or } 398.74 \times 10^{-10} \mathrm{~cm} \end{aligned}$ Volume of unit cell $=\left(398.74 \times 10^{-10} \mathrm{~cm}\right)^3$ For $\begin{aligned} & \text { сср }=2=4, \\ & N_a=6.0 \times 10^{23} \\ & f=\frac{4 \times 64}{\left(398.74 \times 10^{-10} \mathrm{~cm}\right)^3 \times 6.0 \times 10^{23}} \\ & f=6.73 \approx 6.67 \end{aligned}$ Hence, option (a) is correct.

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

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