The radius of a single atom of a genenric element x is 197 pm and a crystal of x has a unit cell that is face centered cubic. calc the volume of the unite cell.
superr confused can you please show all work along with the answer Thank you
google "face centered cubic cell"
the length of the diagonal of a face of the cube is two atom diameters
the cube edge length is √2 times the atom diameter
the volume is the edge length cubed (^3)
So I would square root 197 and put it to the power or three?
Of course! To calculate the volume of the unit cell, we first need to understand the structure of a face-centered cubic (FCC) crystal.
In an FCC crystal, each corner of the cube is shared by eight neighboring unit cells, and each face of the cube is shared by two neighboring unit cells. This arrangement creates a total of four atoms per unit cell.
Given that the radius of a single atom of element X is 197 pm, we can find the side length (a) of the cube using the formula:
a = 2 * r
where r is the radius of the atom. Substituting the given value, we get:
a = 2 * 197 pm
= 394 pm
Now that we know the side length of the cube, we can calculate the volume of the unit cell using the formula:
Volume = a^3
Substituting the value of a, we have:
Volume = (394 pm)^3
= 61,471,144 pm^3
However, it is more convenient to express the volume in cubic centimeters (cm^3). To convert pm^3 to cm^3, we use the fact that 1 cm = 10^10 pm:
Volume = 61,471,144 pm^3 * (1 cm / 10^10 pm)^3
= 61,471,144 cm^3 / 10^30 cm^3
= 6.1471 cm^3
Thus, the volume of the unit cell is approximately 6.1471 cm^3.