Question

A metal crystallises in FCC structure. If the edge length of the unit cell is 300 pm then the radius of the metal atom is approximately​

Answer 1

Given:

A metal crystallises in FCC structure. If the edge length of the unit cell is 300 pm.

To find:

Radius of metal atom?

Calculation:

In FCC structure, we can say:

• Let edge length be 'L' , and radius of atom be 'r'.

$\rm \: \sqrt{ {L}^{2} + {L}^{2} } = (r + r + 2r)$

$\rm \: \implies \sqrt{ {L}^{2} + {L}^{2} } = 4r$

$\rm \: \implies \sqrt{ 2{L}^{2}} = 4r$

$\rm \: \implies L \sqrt{2} = 4r$

$\rm \: \implies r = \dfrac{L \sqrt{2} }{4}$

$\rm \: \implies r = \dfrac{300 \times \sqrt{2} }{4}$

$\rm \: \implies r = 106.06 \: pm$

So radius of atom is approximately 106.06 pm.