The radius of a single atom of generic element X is 197 picometer(pm) and crystal of X has a unit cell that is face centered cubic calc the volume of the unit cell.
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To calculate the volume of the unit cell with a face-centered cubic (FCC) structure, we need to use the formula:
Volume of unit cell = 4 * r^3
Where:
r = radius of the atom
Given that the radius of the atom (r) is 197 picometers (pm), we can substitute this value into the formula:
Volume of unit cell = 4 * (197 pm)^3
Now let's calculate the volume of the unit cell:
Volume of unit cell = 4 * (197 pm)^3
= 4 * (197 pm)(197 pm)(197 pm)
= 4 * 7,717,041 pm^3
= 30,868,164 pm^3
Therefore, the volume of the unit cell is 30,868,164 picometers cubed (pm^3).