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Question

A metal 'X' forms a body centred cubic lattice whose unit cell edge length is 300 pm. Calculate the density of 'X'.
Given: Molar mass of metal 'X' =78 g mol1

A
9.6 g cm3
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B
10.49 g cm3
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C
104.9 g cm3
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D
8.45 g cm3
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Solution

The correct option is A 9.6 g cm3
Length of side of unit cell 'a' =300 pm=300×1010cm
Volume of unit cell =(300×1010cm)3=2.7×1023cm3
The given metal forms a body centred cubic lattice.
Thus,
Number of atoms per unit cell =88+11=2

Density of 'X' =Atomic mass×ZVolume of unit cell×NA
where,
Z = No. of atoms in unit cell
Na = Avagadro number

Density =78×22.7×1023×6.023×1023
ρ=9.5929.6 g/cm3

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