The density of platinum is 21500 kg/m3 and the cell volume is 6.04 x 10-26 L. Determine the number of atoms in the unit cell. Note: the number of atoms in a unit cell is a whole number.
I would convert density in kg/m^3 to g/cc.
Then knowing density and volume (convert volume to cc), calculate mass of the unit cell.
Then #atoms in unit cell*atomic mass Pt/6.022 x 10^23 = mass of unit cell.
The only unknown in that relationship is the # atoms. Calculate that. Post your work if you need further assistance.
To determine the number of atoms in the unit cell, we need to know the volume of one atom in the unit cell and the volume of the unit cell itself.
First, let's convert the given cell volume from liters to cubic meters:
6.04 x 10^(-26) L = 6.04 x 10^(-26) m^3
Next, we need to calculate the volume of one platinum atom in the unit cell. We can do this by assuming each atom in the unit cell occupies an equal volume and assuming the atoms are spherical.
The formula for the volume of a sphere is:
V = (4/3) * π * r^3
Rearranging the formula to solve for radius:
r = (3V / (4π))^(1/3)
Since we want the volume of one atom, we will use half the cell volume to calculate the radius:
V_atom = 0.5 * 6.04 x 10^(-26) m^3
r = (3 * V_atom / (4 * π))^(1/3)
Now, we have the radius, and we can calculate the volume of one atom.
Next, we need to find the atomic volume, which is the ratio of the mass of one atom to its density. The atomic volume can be calculated using the formula:
Atomic volume = (mass of one atom) / (density of the material)
We know the density of platinum is 21500 kg/m^3. To find the mass of one atom, we need to know the atomic mass of platinum. The atomic mass of platinum can be found on the periodic table. The atomic mass of platinum is approximately 195 g/mol.
Converting grams to kilograms:
atomic mass of platinum = 195 g/mol = 0.195 kg/mol
Now, we can calculate the mass of one atom using Avogadro's number (6.022 x 10^23 atoms/mol):
mass of one atom = (0.195 kg/mol) / (6.022 x 10^23 atoms/mol)
Finally, we can calculate the atomic volume:
atomic volume = (mass of one atom) / (density of platinum)
Now, we divide the volume of the unit cell by the atomic volume to find the number of atoms in the unit cell:
Number of atoms = (Volume of unit cell) / (atomic volume)
Plugging in the values and performing the calculations will give us the desired result.