1. Calculate the volume of the nanoparticle:
* Assume the nanoparticle is spherical.
* The volume of a sphere is (4/3)πr³, where r is the radius.
* Radius (r) = 2 nm / 2 = 1 nm = 1 x 10⁻⁹ m
* Volume = (4/3)π(1 x 10⁻⁹ m)³ ≈ 4.19 x 10⁻²⁷ m³
2. Calculate the volume of a single gold atom:
* The atomic radius of gold is approximately 0.144 nm = 1.44 x 10⁻¹⁰ m
* Volume of a single gold atom ≈ (4/3)π(1.44 x 10⁻¹⁰ m)³ ≈ 1.24 x 10⁻²⁹ m³
3. Divide the nanoparticle volume by the volume of a single gold atom:
* Number of atoms ≈ (4.19 x 10⁻²⁷ m³) / (1.24 x 10⁻²⁹ m³) ≈ 338
Therefore, a 2 nm gold nanoparticle would contain approximately 338 gold atoms.
Important Notes:
* This calculation is an approximation. The actual number of atoms in a nanoparticle can vary depending on factors like:
* The exact shape of the nanoparticle (it might not be perfectly spherical).
* The packing density of the atoms within the nanoparticle.
* The presence of other elements or impurities.
* In reality, nanoparticles can be much more complex than simple spheres. They can have different shapes, and their atomic arrangement can be irregular.
