Answer:
7.38 g/cm³ is the density of the metal
Explanation:
In a Face-centered cubic unit cell you have 4 atoms. Also, the edge length is √8×r (r is radius of the atom).
To solve this problem, we need first to calculate the volume of the unit cell and then, with molar mass calculate the mass of 4 atoms. As density is the ratio between mass and volume we can obtain this value.
- <em>Volume of the unit cell</em>
Volume = a³
a = √8×r
(r = 198x10⁻¹²m)
a = 5.6x10⁻¹⁰ m
Volume = 1.756x10⁻²⁸ m³
1m = 100cm → 1m³ = (100cm)³:
1.756x10⁻²⁸ m³× ((100cm)³ / 1m³) =
<h3> 1.756x10⁻²² cm³ → Volume of the unit cell in cm³</h3><h3 />
- <em>Mass of the unit cell:</em>
<em>There are 4 atoms of gold:</em>
4 atoms × (1mol / 6.022x10²³ atoms) = 6.64x10⁻²⁴ moles of gold
As 1 mole weighs 195.08g:
6.64x10⁻²⁴ moles of gold × (195.08g / mol) =
<h3>1.296x10⁻²¹g is the mass of the unit cell</h3><h3 />
- <em>Density of the metal:</em>
1.296x10⁻²¹g / 1.756x10⁻²² cm³ =
<h3>7.38 g/cm³ is the density of the metal</h3>
