in fcc crystal system with unit cell of an edge 200pm calculate its density if 200grams of this element contains 24*10E23
not a complete question.
To calculate the density of a material in a face-centered cubic (FCC) crystal system, we need to know the mass and volume of the unit cell. From these values, we can determine the density using the formula:
Density = mass / volume
First, let's determine the volume of the unit cell.
The unit cell in an FCC crystal system consists of eight atoms, with each atom located at the corners of the cube and one atom located at the center of each face. The length of the edge of the unit cell (a) can be calculated using the formula:
a = 4 * r / √2
where r is the radius of the atoms.
Given that the edge of the unit cell is 200 pm (picometers), we can convert it to meters by dividing by 10^12:
a = 200 pm / (10^12 pm/m)
Next, we need to calculate the radius of the atoms. In an FCC crystal system, the atomic radius is related to the edge length (a) by the equation:
r = √2 * a / 4
Now we can calculate the radius:
r = √2 * (200 pm / 10^12 pm/m) / 4
Having calculated the radius, we can calculate the volume of the unit cell:
Volume = (4/3) * π * r^3
The volume can then be converted to cubic meters by dividing by (10^12 m)^3:
Volume = (4/3) * π * (r^3) / (10^12 m)^3
Now, we can proceed to calculate the density using the given values:
Density = mass / volume
The mass is given as 200 grams, and the number of atoms is 24 * 10^23.
I'll perform the calculations: