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

\frac{4}{3} π r^{3}

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\frac{8}{3} π r^{3}

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\frac{16}{3} π r^{3}

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\frac{64 r^{3}}{3 \sqrt{3}}

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Solution

The correct option is C $\frac{16}{3} π r^{3}$

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

Volume of 1 spherical atom is $\frac{4}{3} π r^{3}$ .

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

Hence, the correct option is $C$

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Similar questions

Question 1
If the radius of a sphere is 2r, then its volume will be:

A) $\frac{4}{3} π r^{3}$
B) $4 π r^{3}$
C) $\frac{8}{3} π r^{3}$
D) $\frac{32}{3} π r^{3}$

The volume of atoms (radius r) present in fcc unit cell of metal is:

Q. If

V = \frac{4}{3} π r^{3}

, at what rate in cubic units is

V

increasing when

r = 10

and

\frac{d r}{d t} = 0.1

If $V = \frac{4}{3} π r^{3}$ ,at what rate in cubic units is V increasing when r = 10 and $\frac{d r}{d t} = 0.01$ ?

Q. The volume of a sphere is

\frac{4}{3} π r^{3}

cubic units, then the ratio of the volume of a cube to that of a sphere which will fit inside the cube is:

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

The correct option is C 163πr3In fcc unit cell, no. of atoms are =[6×12]+[8×18]=4Volume of 1 spherical atom is 43πr3.So, volume occupied by atoms in fcc unit cell will be 4×43πr3=163πr3, where, r is radius of atom.Hence, the correct option is C