Single Choice

In face centred cubic unit cell, what is the volume occupied?

A$$\dfrac{4}{3}\pi r^3$$
B$$\dfrac{8}{3}\pi r^3$$
C$$\dfrac{16}{3}\pi r^3$$
Correct Answer
D$$\dfrac{64 r^3}{3\sqrt{3}}$$

Solution


In fcc unit cell, no. of atoms are $$=[6 \times \dfrac{1}{2}] + [8 \times \dfrac{1}{8}] = 4$$

Volume of 1 spherical atom is $$\dfrac { 4 }{ 3 } \pi { r }^{ 3 }$$.

So, volume occupied by atoms in fcc unit cell will be $$4\times \dfrac { 4 }{ 3 } \pi { r }^{ 3 }=\dfrac { 16 }{ 3 } \pi { r }^{ 3 }$$, where, r is radius of atom.

Hence, the correct option is $$\text{C}$$

SIMILAR QUESTIONS

Solid State

The maximum percentage of available volume that can be filled in a face centred cubic system by an atom is:

Solid State

An element X (atomic weight $$= 24$$ g/mol) forms a face centered cubic lattice. If the edge length of the lattice is $$4\times10^{-8}$$ cm and the observed density is $$2.40 \times10^{3}$$ g cm$$^{-3}$$, then the percentage occupancy of lattice points by element X is : (Use $$N_A=6\times10^{23}$$)

Solid State

An element X (atomic weight $$= 24$$ amu) forms a face-centred cubic lattice. If the edge length of the lattice is $${4\times10^{- 8}}$$ cm and the observed density is $$2.40 \times 10^{3}$$ kg m$$^{-3}$$, then the percentage occupancy of lattice points by element X is: (use $$ {N_{A}= 6\times 10^{23}}$$)

Solid State

Packing fraction of an identical solid sphere is $$74\%$$ in:

Solid State

The fraction of volume occupied by atoms in a face centered cubic unit cell is :

Solid State

The neon atoms has a radius of $$160\,pm.$$ What is the edge of the unit cell of a face centered structured of neon ?

Solid State

Silver crystallizes in a fcc lattice and has a density of $$10.6 \,g/cm^3$$. What is the length of an edge of the unit cell ?

Solid State

There are three cubic unit cells $$A, B$$ and $$C$$. $$A$$ is FCC and all of its tetrahedral voids are also occupied. $$B$$ is also FCC and all of its octahedral voids are also occupied. $$C$$ is simple cubic and all of its cubic voids are also occupied. If voids in all unit cells are occupied by the spheres exactly at their limiting radius, then the order of packing efficiency would be

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