Acertain metal m crystallizes in a lattice described by a body-centered cubic (bcc) unit cell. the lattice constant a has been measured by x-ray crystallography to be 409. calculate the radius of an atom of m.

The radius of the atom is 177.1

Explanation:

A Body-centered cubic lattice (bcc), like all lattices, has lattice points at the eight corners of the unit cell plus an additional points at the center of the cell.

For a body-centered cubic (bcc) unit cell, the formula below can be used to obtain the radius of the atom

a = 4r/√3

where;

a is lattice constant = 409

r is the radius of metal M = ?

From the equation above, make 'r' the  subject of formula

r = (a√3)/4

r = (409*√3)/4

r = 177.1

Therefore, the radius of the atom is 177.1