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

  • Option 1)

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

  • Option 2)

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

  • Option 3)

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

  • Option 4)

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

 

Answers (1)

As discussed in

No. of atoms(z) for face centered unit cell -

Lattice points: at corners and face centers of unit cell.

For face centered cubic (FCC), z=4.

- wherein

 

 V=n\times \frac{4}{3}\pi r^{3}

4\times \frac{4}{3}\pi r^{3}

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


Option 1)

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

Option is incorrect

Option 2)

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

Option is incorrect

Option 3)

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

Option is incorrect

Option 4)

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

Option is correct

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