Question

lithium crystallizes in a body-centered cubic crystal. if the length of the side of the unit cell is 350 pm, the minimum distance between the two Li atoms will be​

Answer 1

Given:

Lithium crystallizes in a body-centered cubic crystal. The length of the side of the unit cell is 350 pm.

To find:

Minimum distance between two Li atoms?

Calculation:

In BCC lattice, the relationship between edge length and radius of atom is as follows:

$\rm \: 4r = a \sqrt{3}$

• 'r' is radius of atom, 'a' is edge length.

$\rm\implies r = \dfrac{a \sqrt{3} }{4}$

$\rm\implies r = \dfrac{350 \times \sqrt{3} }{4}$

$\rm\implies r \approx 151.5 \: pm$

Now, the minimum distance between 2 Lithium atoms will be equal to twice the radius of each atom.

$\rm \: d_{min} = 2r$

$\rm \implies \: d_{min} = 2 \times 151.5$

$\rm \implies \: d_{min} = 303.1 \: pm$

So, minimum distance will be 303.1 pm.