The radius of a lead atom is 180 pm. Find the density of metallic lead
(Hint: lead is an FCC metal)
so, what is the volume of a lead atom?
what is the mass of a lead atom?
How are they packed? Since the crystal lattice affects density on a large scale, maybe you just want the density of a single atom.
In any case, density = mass/volume
To find the density of metallic lead, we need to know the formula for the volume of a unit cell in the face-centered cubic (FCC) crystal structure. In the FCC structure, each corner atom is shared between eight adjacent unit cells, and each face atom is shared between two adjacent unit cells.
The formula for the volume of a unit cell in an FCC structure is given by:
V = (4/3) * r³ * N
where V is the volume, r is the radius of the atom, and N is the Avogadro's number (6.022 x 10^23 atoms/mol).
Given that the radius of a lead atom is 180 pm, we convert it to meters by using the conversion factor: 1 pm = 1 x 10^-12 m.
Therefore, the lead atom radius in meters is:
r = 180 pm * (1 x 10^-12 m/pm) = 1.8 x 10^-10 m
Next, we can substitute the values into the formula to calculate the volume of the unit cell:
V = (4/3) * (1.8 x 10^-10 m)³ * (6.022 x 10^23 atoms/mol)
Now, we need to find the molar mass of lead, which is 207.2 g/mol. The molar mass tells us how many grams of lead are in one mole (Avogadro's number) of lead atoms.
To calculate the density, we use the equation:
density = mass / volume
The mass can be calculated by:
mass = molar mass * number of moles
Number of moles = (number of atoms) / (Avogadro's number)
In one unit cell, there are 4 atoms (one at each corner), so the number of atoms is 4.
Substituting the values into the equations, we can find the density of metallic lead.