Question

Silver has an atomic radius of 144 picometre and the density of silver is 10.6 gram per centimetre cube to which type of cubic crystal silver belongs

Answer 1

Answer:

Silver belongs to the face centered cubic crystal.

Explanation:

Number of atom in unit cell =Z

Density of silver = $10.6 g/cm^3$

radius of the silver = r = 144 pm

Atomic mass of silver (M) = 107.87 g/mol

Formula used :  

$\rho=\frac{Z\times M}{N_{A}\times a^{3}}$

where,

$\rho$ = density

Z = number of atom in unit cell

M = atomic mass

$(N_{A})$ = Avogadro's number  

a = edge length of unit cell

On substituting all the given values , we will get the value of 'Z'.

When Z = 1, simple cubic unit cell

a =2r =2 × 144 pm = 288 pm = $2.88\times 10^{-8} cm$

$10.6 g/cm3=\frac{1\times 107.87 g/mol}{6.022\times 10^{23} mol^{-1}\times (2.88\times 10^{-8} cm)^{3}}$

$10.6 g/cm3$ ≠ $7.49 g/cm^3$

When Z = 4, simple face centered cubic unit cell

$a=2.828\times r=2.828\times 144 pm=4.07\times 10^{-8} cm$

$10.6 g/cm3=\frac{4\times 107.87 g/mol}{6.022\times 10^{23} mol^{-1}\times (4.07\times 10^{-8} cm)^{3}}$

$10.6 g/cm3$ =  $10.6 g/cm^3$

When Z = 2, simple body centered cubic unit cell

$a=2.309\times r=2.309\times 144 pm=3.32\times 10^{-8} cm$

$10.6 g/cm3=\frac{2\times 107.87 g/mol}{6.022\times 10^{23} mol^{-1}\times (3.32\times 10^{-8} cm)^{3}}$

$10.6 g/cm3$ ≠ $9.78 g/cm^3$

Silver belongs to the face centered cubic crystal.