Question

The relation between radius of sphere and edge length in simple cubic lattice is ______.

Options

• `sqrt3r = 4a`

• `sqrt3a = 4r`

• `r = a/2`

• `sqrt2a = 4r`

Answer 1

The relation between radius of sphere and edge length in simple cubic lattice is `bbunderline(r = a/2)`.

Explanation:

In a Simple Cubic Lattice (SCL), atoms are arranged at each corner of the cube.

Each corner atom touches the next corner atom directly along the edge of the cube.

That means one complete atom fits along the edge, with half of one atom at one corner and half at the other.

If r is the atomic radius and a is the edge length of the cube, then:

Edge length (a) = 2r

Because the two atoms (from adjacent corners) contribute one full diameter (2r) across the edge.

So, rearranging:

r = `a/2`

This is the relation between radius (r) and edge length (a) in a Simple Cubic Unit Cell.