Advertisements
Advertisements
Question
A face centred cube (FCC) consists of how many atoms? Explain
Advertisements
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
A unit cell of iron crystal has edge length 288 pm and density 7.86 g.cm-3. Find the number of atoms per unit cell and type of the crystal lattice.
Given : Molar mass of iron = 56 g.mol-1; Avogadro's number NA = 6.022 x 1023.
How many atoms constitute one unit cell of a face-centered cubic crystal?
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 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?
Distinguish between Hexagonal and monoclinic unit cells
Distinguish between Face-centred and end-centred unit cells.
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?
How can you determine the atomic mass of an unknown metal if you know its density and the dimension of its unit cell? Explain.
Explain with reason sign conventions of ΔS in the following reaction
N2(g) + 3H2(g) → 2NH3(g)
Explain with reason sign conventions of ΔS in the following reaction
CO2(g) → CO2(g)
Calculate the number of unit cells in 8.1 g of aluminium if it crystallizes in a f.c.c. structure. (Atomic mass of Al = 27 g mol–1)
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 ____________.
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.
An element (atomic mass 100 g/mol) having bcc structure has unit cell edge 400 pm. The density of element is (No. of atoms in bcc, Z = 2).
The number of atoms contained in a fcc unit cell of a monoatomic substance is ____________.
Edge length of unit cell of chromium metal is 287 pm with a bcc arrangement. The atomic radius is of the order:
An element with atomic mass 100 has a bcc structure and edge length 400 pm. The density of element is:
The percentage of empty space in a body centred cubic arrangement is ______.
Match the type of unit cell given in Column I with the features given in Column II.
| Column I | Column II |
| (i) Primitive cubic unit cell | (a) Each of the three perpendicular edges compulsorily have the different edge length i.e; a ≠ b ≠ c. |
| (ii) Body centred cubic unit cell | (b) Number of atoms per unit cell is one. |
| (iii) Face centred cubic unit cell | (c) Each of the three perpendicular edges compulsorily have the same edge length i.e; a = b = c. |
| (iv) End centred orthorhombic cell | (d) In addition to the contribution from unit cell the corner atoms the number of atoms present in a unit cell is one. |
| (e) In addition to the contribution from the corner atoms the number of atoms present in a unit cell is three. |
The correct set of quantum numbers for 3d subshell is
The coordination number for body center cubic (BCC) system is
The correct set of quantum numbers for 2p sub shell is:
Percentage of free space in body centred cubic unit cell is
A solid is formed by 2 elements P and Q. The element Q forms cubic close packing and atoms of P occupy one-third of tetrahedral voids. The formula of the compound is ______.
The ratio of number of atoms present in a simple cubic, body-centred cubic and face-centred cubic structure are, respectively ______.
