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Silver crystallises in F.C.C. (face-centred cubic crystal) structure. The edge length of the unit cell is found to be 408.7 pm. Calculate density of the unit cell. - Chemistry

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Silver crystallises in F.C.C. (face-centred cubic crystal) structure. The edge length of the unit cell is found to be 408.7 pm. Calculate density of the unit cell.

[Given: Molar mass of silver is 108 g mol-1 ]

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Solution

Given: Edge length (a) = 408.7 pm = 408.7 x 10–12 m = 408.7 x10-10 cm,
Molar mass/Atomic mass of silver = 108 g mol-1
To find: Density (d)

Formulae:

`1."Mass of one atom"="Atomic mass"/"Avogardo Number"`

`2. Volume of unit cell=a^3`

`3. "Density"="mass of unit cell"/"Volume of unit cell" `

Calculation: For fcc lattice, number of atoms per unit cell is 4.

Mass of one atom of silver=`"Atomic mass"/"Avogadro number"`

`=108/(6.023xx10^23)=17.9xx10^(-23)g`

Mass of unit cell = 4 x 17.9 x 10–23 = 71.7 x 10–23 g

Volume of unit cell = a3 = (408.7 x 10–10 cm)3 = 6.827 x10–23 cm3

`"Density"="mass of unit cell"/"Volume of unit cell" `

`=(71.7xx10^(-23)g)/(6.827xx10^(-23)cm^3)=10.5g `

Notes

The above numerical can also be solved using the formula, `d=(z.M)/(a^3N_A)`

Concept: Solid State Numericals
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