a metal crystallizes with a face-centered cubic lattice.The edge of the unit cell is `408` pm. The diameter of the metal atom is :

Options

A. `288p m`
B. `408 p m`
C. `144p m`
D. `204p m`

Answer

1

Explanation

In a face -centered cubic lattice. the atom of the face centre is in touch with the other two atoms diagonally arranged at the corners. The length of the face diagonal is `sqrt(2)a` As all the three spheres along the face diagonal touch each other, the length of the body diagonal is also equal to `4r` where `r` is the radius of the sphere (atom). Therefore
`4r=sqrt(2)a`
or `r=(sqrt(2))/(4)a=(a)/(2sqrt(2))`
the diameter `(d)` of the metal atom is `2r`.Therefore
`d=2r=(a)/(sqrt(2))=(408p m)/(1.414)`
`=288p m`