Advertisements
Advertisements
Question
A face centred cube (FCC) consists of how many atoms? Explain
Solution
Face-centred cubic lattice (fcc):
1) In face-centred cubic unit cell, eight constituent particles (spheres) are present at eight corners of unit cell. Six constituent particles (spheres) are present at centres of six faces
2) A constituent particle present at a corner is shared by eight neighbouring unit cells. Its contribution to a unit cell is only 1/8. Thus, the number of atoms present at corners per unit cell
= 8 corner atoms x 1/8 atom per unit cell = 1
3) A constituent particle present at the centre of a face is shared by two neighbouring unit cells. Its contribution to a unit cell is only 1/2.
The number of atoms present at faces per unit cell
= 6 atoms at the faces x 1/2 atom per unit cell = 3
4) The total number of atoms per unit cell = 1 + 3 = 4
Thus, a face-centred cubic unit cell has 4 atoms per unit cell.
APPEARS IN
RELATED QUESTIONS
Gold occurs as face centred cube and has a density of 19.30 kg dm-3. Calculate atomic radius of gold (Molar mass of Au = 197)
Face centred cubic crystal lattice of copper has density of 8.966 g.cm-3. Calculate the volume of the unit cell. Given molar mass of copper is 63.5 g mol-1 and Avogadro number NA is 6.022 x 1023 mol-1
An element crystallises in a b.c.c lattice with cell edge of 500 pm. The density of the element is 7.5g cm-3. How many atoms are present in 300 g of the element?
An element with molar mass 27 g mol−1 forms a cubic unit cell with edge length 4.05 ✕ 10−8 cm. If its density is 2.7 g cm−3, what is the nature of the cubic unit cell?
An element with molar mass 2.7 × 10-2 kg mol-1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7 × 103 kg m−3, what is the nature of the cubic unit cell?
What is the coordination number of atoms:
(a) in a cubic close-packed structure?
(b) in a body-centred cubic structure?
How can you determine the atomic mass of an unknown metal if you know its density and the dimension of its unit cell? Explain.
An element has atomic mass 93 g mol–1 and density 11.5 g cm–3. If the edge length of its unit cell is 300 pm, identify the type of unit cell
An element 'X' (At. mass = 40 g mol-1) having f.c.c. the structure has unit cell edge length of 400 pm. Calculate the density of 'X' and the number of unit cells in 4 g of 'X'. (NA = 6.022 × 1023 mol-1)
The density of silver having an atomic mass of 107.8 g mol- 1 is 10.8 g cm-3. If the edge length of cubic unit cell is 4.05 × 10- 8
cm, find the number of silver atoms in the unit cell.
( NA = 6.022 × 1023, 1 Å = 10-8 cm)
The number of atoms per unit cell in a body centered cubic structure is ____________.
An atom located at the body center of a cubic unit cell is shared by ____________.
Volume of unit cell occupied in face-centered cubic arrangement is ____________.
TiCl has the structure of CsCl. The coordination number of the ions in TiCl is ____________.
An element forms a cubic unit cell with edge length 405 pm. Molar mass of this element is 2.7 × 10−2 kg/mol and its density is given as 2.7 × 103 kg/m3. How many atoms of these elements are present per unit cell?
A metal has a body-centered cubic crystal structure. The density of the metal is 5.96 g/cm3. Find the volume of the unit cell if the atomic mass of metal is 50.
Gold has a face-centered cubic lattice with an edge length of the unit cube of 407 pm. Assuming the closest packing, the diameter of the gold atom is ____________.
Sodium metal crystallizes in a body-centered cubic lattice with a unit cell edge of 4.29 Å. The radius of the sodium atom is approximate:
The empty space in the body-centered cubic lattice is ____________.
The number of atoms contained in a fcc unit cell of a monoatomic substance is ____________.
The density of a metal which crystallises in bcc lattice with unit cell edge length 300 pm and molar mass 50 g mol−1 will be:
The percentage of empty space in a body centred cubic arrangement is ______.
Percentage of free space in body centred cubic unit cell is
