Question

lithium crystallizes as body centered cubic crystal. If the length of the side of unit cell is 350pm, the minimum distance between two Li atoms will be?

(a) 150√2pm.
(b) 150√3pm.
(c) 175√2pm.
(d) 175√3pm​

Answer 1

Answer:

            (d) 175√3 pm​

Explanation:

Given:

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

To find:

      The minimum distance between two Li atoms?

Calculation:

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

                               $4r= a\sqrt{3}$

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

⇒ $r = \frac{a\sqrt[]{3} }{4}$

⇒ $r = \frac{350 X \sqrt{ 3} }{4}$

⇒ $r$ ≈ 151.5 pm

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

                   $d_{min} = 2r$

⇒ $d_{min}=2$ x 151.5

⇒ $d_{min} = 303.1$ pm

So, the minimum distance will be 303.1 pm = $175\sqrt{3}$ pm.

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