To calculate the number of atoms in a given volume of aluminum, we need to use the concept of molar volume and Avogadro's number.
First, let's convert the dimensions of the cube from centimeters to meters:
Length = 2.0 cm = 0.02 m
Width = 2.0 cm = 0.02 m
Height = 2.0 cm = 0.02 m
Next, we need to calculate the volume of the cube:
Volume = Length * Width * Height
Volume = 0.02 m * 0.02 m * 0.02 m
Volume = 0.000008 m³
Now, we can calculate the number of moles using the density of aluminum:
Density = Mass / Volume
Mass = Density * Volume
Mass = 2700 kg/m³ * 0.000008 m³
Mass = 0.0216 kg
To find the number of moles (n), we use the formula:
n = Mass / molar mass
The molar mass of aluminum is approximately 27 g/mol, which is 0.027 kg/mol.
n = 0.0216 kg / 0.027 kg/mol
n ≈ 0.8 mol
Now, we can use Avogadro's number, which is approximately 6.022 × 10^23 atoms/mol, to calculate the number of atoms:
Number of atoms = n * Avogadro's number
Number of atoms ≈ 0.8 mol * (6.022 × 10^23 atoms/mol)
Number of atoms ≈ 4.818 × 10^23 atoms
Therefore, there are approximately 4.818 × 10^23 atoms in a 2.0 cm x 2.0 cm x 2.0 cm cube of aluminum.