Total volume of atoms present in a face­-centred cubic unit cell of a metal is (r is atomic radius )

  • Option 1)

    \frac{20}{3}\pi r^{3}

  • Option 2)

    \frac{24}{3}\pi r^{3}

  • Option 3)

    \frac{12}{3}\pi r^{3}

  • Option 4)

    \frac{16}{3}\pi r^{3}

 

Answers (2)

As we learnt in

Packing fraction for face centered cubic unit cell -

Pf = 0.74

-

 

 

 

In case of a face­centred cubic structure, since our atoms are present in a unit cell, hence volume

V=4\left ( \frac{4}{3}\pi r^{3} \right )\frac{16}{3}\pi r^{3}

Correct option is 4.


Option 1)

\frac{20}{3}\pi r^{3}

This is an incorrect option.

Option 2)

\frac{24}{3}\pi r^{3}

This is an incorrect option.

Option 3)

\frac{12}{3}\pi r^{3}

This is an incorrect option.

Option 4)

\frac{16}{3}\pi r^{3}

This is the correct option.

N neha

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