Question

The radius of silver atom is 143.5 pm and it crystallises in face centred cubic arrangement. (Atomic mass of Ag = 107.47, N_A = 6.023 × 10²³)

What is the density of silver metal?

विकल्प

• 5.36 g/cm³

• 8.60 g/cm³

• 10.72 g/cm³

• 7.07 g/cm³

Answer 1

10.72 g/cm³

Explanation:

Given: Radius of silver atom (r) = 143.5 pm

Face-centred cubic (fcc) structure ⇒ Z = 4 atoms/unit cell

Atomic mass (M) = 107.47 g/mol

Avogadro’s number, N_A = 6.023 × 10²³ mol⁻¹

To find: Density (ρ) = ?

For fcc,

`a = (4 r)/sqrt 2`

`a = (4 xx 143.5)/1.414`

= 405.8 pm

= 4.058 × 10⁻⁸ cm

We know that

`rho = (Z xx M)/(N_A xx a^3)`

`rho = (4 xx 107.47)/(6.023 xx 10^23 xx (4.058 xx 10^-8)^3)`

`rho = 429.88/(6.023 xx 10^23 xx 66.82 xx 10^-24)`

`rho = 429.88/(6.023 xx 66.82 xx 10^-1)`

`rho = 429.88/(6.023 xx 6.682)`

`rho = 429.88/40.24`

`rho = 429.88/40.27`

= 10.68 ≈ 10.7 g/cm³