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# Solution for 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. - HSC Science (General) 12th Board Exam - Chemistry

ConceptCalculations Involving Unit Cell Dimensions

#### 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

2016-2017 (July) (with solutions)
Question 4.1 | 7.00 marks

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Solution 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.
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