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Question

A metal crystallises into two cubic phases, face-centred cubic (fcc) and body-centred cubic (bcc) whose unit lengths are 3.5 and 3.0 $$\mathring{A}$$ respectively. Calculate the ratio of densities of fcc and bcc.


Solution

Density of fcc $$= \dfrac {Z_{1}\times At. mass}{Av. no.\times V_{1}}$$

and density in bcc $$= \dfrac {Z_{2} \times At. mass}{Av. no.\times V_{2}}$$

$$\dfrac {d_{fcc}}{d_{bcc}} = \dfrac {Z_{1}}{Z_{2}} \times \dfrac {V_{2}}{V_{1}}$$

For fcc $$Z_{1} = 4; V_{1} = a^{3} = (3.5\times 10^{-8})^{3}$$

For bcc $$Z_{2} = 2; V_{2} = a^{3} = (3.0\times 10^{-8})^{3}$$

$$\dfrac {d_{fcc}}{d_{bcc}} = \dfrac {4\times (3.0\times 10^{-8})^{3}}{2\times (3.5\times 10^{-8})^{3}} = 1.259$$

Chemistry

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