Strontium has density of 2.64 and crystallizes with the face-centered cubic unit cell. Find the radius of the strontium atom
mass unit cell = 4*molar mass/6.022E23
volume = mass/density. Solve for volume.
a = volume1/3
Then 4r = a*21/2
idk how do explain it to you but i figured out that it is 200 picometers.
219
To find the radius of the strontium atom, we can utilize the face-centered cubic (FCC) unit cell structure.
In an FCC unit cell, the atoms are arranged in such a way that each corner of the cube has a constituent atom, and there is an additional atom in the center of each face of the cube. This results in a total of 4 atoms per unit cell.
The formula for the atomic radius (r) in an FCC lattice can be determined using the lattice parameter (a) as follows:
r = √(2) * (a / 4)
Here, the lattice parameter (a) represents the edge length of the unit cell.
To proceed, we need to use the given information about the density of strontium (denoted as ρ) and its relationship with the lattice parameter. The density of a material is defined as its mass (m) divided by its volume (V):
ρ = m / V
The volume of an FCC unit cell can be expressed in terms of the lattice parameter (a):
V = (a^3) / 4
To determine the lattice parameter, we need to rewrite the density equation as:
a = (4 * (m / ρ))^(1/3)
Now we can substitute this value of a into the equation for the atomic radius:
r = √(2) * ((4 * (m / ρ))^(1/3) / 4)
Finally, substituting the given density of strontium (2.64 g/cm³) and the molar mass of strontium (88.906 g/mol), we can calculate the radius of the strontium atom.
Note: The molar mass of strontium is used as the mass (m) in the calculations since we are interested in the size of an individual atom.
Let's proceed with the calculations: