Advertisements
Advertisements
Question
Answer the following in brief.
Calculate the number of atoms in fcc unit cell.
Advertisements
Solution
- A face-centred cubic (fcc) unit cell has particles at the eight corners plus particles at the centre of its six faces.
- Each particle present at the corner of a given unit cell is shared with seven other neighbouring unit cells. As a result, its contribution to the given unit cell is only `1/8`.
Thus, the number of particles present at corners per unit cell
= 8 corner atoms `xx 1/8` atom per unit cell = 1 - Each particle at the centre of the six faces is shared with one neighbouring cube. Thus, 1/2 of each face particle belongs to the given unit cell.
Thus, the number of particles present at faces per unit cell
= 6 atoms at the faces `xx 1/2` atom per unit cell = 3
Therefore, fcc unit cell has one corner particle plus 3 face particles, making total of 4 particles per unit cell.
APPEARS IN
RELATED QUESTIONS
An element with molar mass 27 g/mol forms a cubic unit cell with edge length of 405 p.m. If the density of the element is 2.7 g/cm3, what is the nature of the cubic unit cell?
Write the relationship between radius of atom and edge length of fcc unit cell.
Give the percentage of empty space in bcc lattice.
Calculate the number of unit cells in 0.3 g of a species having density of 8.5 g/cm3 and unit cell edge length 3.25 × 10-8 cm.
Derive the relationship between density of substance, its molar mass, and the unit cell edge length. Explain how you will calculate the number of particles, and a number of unit cells in x g of metal.
What is the percentage of unoccupied space in fcc unit cell?
In bcc unit cell, the edge length (a) and radius of sphere (r) are related to each other by equation:
An element (atomic mass M g/mol) having bcc structure has unit cell edge 400 pm. The density of the element is ____________ g/cm3.
[NA = 6.0 × 1023 atom mol−1)
An element crystallizes bcc type of unit cell, the density and edge length of unit cell is 4 g cm−3 and 500 pm respectively. What is the atomic mass of an element?
An element with density 2.8 g cm−3 forms fcc unit cell having edge length 4 × 10−8 cm. Calculate molar mass of the element.
Consider the following unit cell.
The number of particles (spheres) per unit cell is:
A metallic element has a cubic lattice with edge length of unit cell 2 Å. Calculate the number of unit cells in 200 g of the metal, if density of metal is 2.5 g cm-3?
Which of the following formulae is used to find edge length of bee unit cell?
What is the density of iron crystal which crystallizes in body-centred cubic structure with edge length 287 pm? (At. mass of Fe = 56 amu)
The coordination number of atoms in body-centred cubic structure (bcc) is ______.
Gold crystallises into face-centred cubic cells. The edge length of a unit cell is 4.08 × 10–8 cm. Calculate the density of gold. [Molar mass of gold = 197 g mol–1]
An element has a bee structure with unit cell edge length of 288 pm. How many unit cells and number of atoms are present in 200 g of the element?
Identify unit cell from following having four particles in it
What is the density of potassium, if it has a bcc structure with edge length 4Å?
(Atomic mass of K = 39)
The correct sequence of the atomic layers in cubic close packing is ______.
The total number of different primitive unit cells is ______.
What would be the empirical formula of a compound having a unit cell containing A ion shared equally at the corner of the cube and B ion on the centre of faces of the cube?
The cubic unit cell of a metal (molar mass = 63.55g mol−1) has an edge length of 362 pm. Its density is 8.92g cm−3.
The type of unit cell is ______.
Calculate the molar mass of an element having a density of 19.2 g cm−3 if it forms an fcc structure [a3 × NA = 40 cm3 mol−1].
