#### Question

A metal crystallises into two cubic faces namely face centered (FCC) and body centered (BCC), whose unit cell edge lengths are 3.5 Å and 3.0 Å respectively. Find the ratio of the densities of FCC and BCC.

#### Solution

Edge length of FCC unit cell (a1) = 3.5 Å

Edge length of BCC unit cell (a2) = 3.0 Å

Density of unit cell = `d=(ZxxM)/(N_Axxa^3)g cm^-3`

Density of FCC unit cell = `d_1=(4xxM)/(N_Axx(3.5A)^3)`

Density of BCC unit cell = `d_2=(2xxM)/(N_Axx(3.0A)^3)`

Ratio of densities of FCC and BCC unit cell is,

`d_1/d_2=(4xxM)/(N_Axx(3.5A)^3) xx (N_Axx(3.0A)^3)/(2xxM)`

`d_1/d_2=54/42.875=1.259~~1.26`

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#### APPEARS IN

Solution for question: A metal crystallises into two cubic faces namely face centered (FCC) and body centered (BCC), whose unit cell edge lengths are 3.5 Å and 3.0 Å respectively. Find the ratio of the densities of FCC and BCC. concept: Calculations Involving Unit Cell Dimensions. For the courses HSC Science (Computer Science), HSC Science (General) , HSC Science (Electronics)