JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Solid State

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A metal M crystallizes into two lattices:- face centred cubic (fcc) and body centred cubic (bcc) with unit cell edge length of 2.0 and 2.5 Å respectively. The ratio of densities of lattices fcc to bcc for the metal M is ______. (Nearest integer)

Answer: 4

Solution

The density of a cubic crystal is

ρ = \frac{Z M}{N _{A} a ^{3}}

, and for the same metal both

M

and

N_{A}

cancel in a ratio. A face-centred cell contains four atoms and a body-centred cell two, so

\frac{ρ _{f cc}}{ρ _{b cc}} = \frac{Z _{f cc}}{Z _{b cc}} \times \frac{a _{b cc}^{3}}{a _{f cc}^{3}} = \frac{4}{2} \times \frac{( 2.5 ) ^{3}}{( 2.0 ) ^{3}} = 2 \times \frac{15.625}{8} = 3.91

. To the nearest integer the ratio of densities is

4

JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Integer answer

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