Question

Sodium crystallises in a body-centred cubic unit cell. (bcc) with edge length 4.29 A. what is the radius of the sodium atom? What is the length of the body diagonal of the unit cell?

Options

• \[\ce{7.44 \overset{\circ}{A}}\]

• \[\ce{1.86 \overset{\circ}{A}}\]

• \[\ce{3.55 \overset{\circ}{A}}\]

• \[\ce{5.75 \overset{\circ}{A}}\]

Answer 1

\[\ce{7.44 \overset{\circ}{A}}\]

Explanation:

For a body centred cubic unit cell (bcc)

Radius (r) = `(a + sqrt(3))/4`

= \[\ce{(4.23 \overset{\circ}{A}) × (1.732)/4}\]

= \[\ce{1.86 \overset{\circ}{A}}\]

Length of the body diagonal = `4r`

= `4 xx 1.86`

= \[\ce{7.44 \overset{\circ}{A}}\]