Question

How do I calculate the number of atoms in one spherical particle of iron that is used in recording media that is 3nm in diameter, the density of iron is given as 7.8g/cm cubed, the atomic mass is 55.847kg/m squared?

Answer 1

To calculate the number of atoms in a spherical particle of iron, we need to use the diameter of the particle, the density of iron, and the atomic mass of iron. Here's the step-by-step calculation:

1. Convert the diameter of the particle from nanometers (nm) to meters (m): Diameter = 3 nm = 3 × 10^-9 m

2. Calculate the volume of the spherical particle using the formula: Volume = (4/3) × π × (Radius)^3

Since we have the diameter, we need to divide it by 2 to get the radius: Radius = Diameter / 2

3. Calculate the volume of the spherical particle: Volume = (4/3) × π × (Radius)^3

4. Convert the density of iron from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³): Density = 7.8 g/cm³ = 7.8 × 10^3 kg/m³

5. Calculate the mass of the spherical particle using the formula: Mass = Volume × Density

6. Convert the atomic mass of iron from kilograms per square meter (kg/m²) to kilograms (kg): Atomic mass = 55.847 kg/m² = 55.847 × 10^-3 kg

7. Calculate the number of moles of iron using the formula: Number of moles = Mass / Atomic mass

8. Calculate the number of atoms using Avogadro's number: Number of atoms = Number of moles × Avogadro's number

Now let's perform the calculations:

Radius = (3 × 10^-9 m) / 2 = 1.5 × 10^-9 m

Volume = (4/3) × π × (1.5 × 10^-9 m)^3

Mass = Volume × Density = [(4/3) × π × (1.5 × 10^-9 m)^3] × (7.8 × 10^3 kg/m³)

Number of moles = Mass / Atomic mass = [(4/3) × π × (1.5 × 10^-9 m)^3 × (7.8 × 10^3 kg/m³)] / (55.847 × 10^-3 kg)

Number of atoms = Number of moles × Avogadro's number

After performing these calculations, you will obtain the number of atoms in one spherical particle of iron with a 3 nm diameter.