Question

Question No. 50
If a is the edge length of a simple cubic unit cell then the distance between two nearest atoms is​

Answer 1

Distance between two nearest atoms = 0.707a

Explanation:

Given: a is the edge length of a simple cubic unit cell.

Find: The distance between two nearest atoms.

Solution: The distance between two nearest atoms in a cubic unit cell will be the distance between an atom at the corner and an atom at the center.

d = 1/2 of the length of the diagonal

   = 1/2 (√2a) as per Pythagoras theorem as the diagonal is the hypotenuse.  d = a √2 / 2 = (1/√2)a = (1/1.414)a = 0.707a.

Answer 2

The distance between the two nearest atoms in a simple cubic unit cell is 'a'.

- In a simple cubic unit cell, the atoms are present only at the corners.

- The nearest distance is measured by the distance between the centres of the two atoms.

- The centre of each atom lies at a corner in a simple cubic unit cell.

- So, the distance between two nearest atoms is equal to the edge length, i.e., 'a'.