An element crystalline in face centred cubic lattice. CCalculate the length of the side of the unit cell if the radius of atom is200pm
a = 4r/(2)^1/2
a = 4*200/1.414 = ?
45
To calculate the length of the side of the unit cell for a face-centered cubic (FCC) lattice, we need to use the relationship between the lattice constant (a) and the radius of the atom (r).
In an FCC lattice, each corner of the cube contains an atom, and there is an additional atom in the center of each face. The atoms touch each other along the body diagonals of the cube.
The relationship between the lattice constant and the atomic radius in an FCC lattice is given by:
a = 4√2 * r
where a is the lattice constant and r is the radius of the atom.
In this case, the radius of the atom is given as 200 pm (picometers), so we can substitute that into the equation:
a = 4√2 * 200 pm
To simplify the calculation, we'll convert the picometers to angstroms (Å). There are 100 picometers in 1 angstrom, so:
a = 4√2 * (200 pm / 100 pm) = 4√2 * 2 Å = 8√2 Å
Therefore, the length of the side of the unit cell for an element with a radius of 200 pm in an FCC lattice is approximately 8√2 angstroms.