A given metal crystalline out with a cubic structure having edge length of `361` pm .if there are four metal atoms in one unit cell, what is the radius of metal atom?

Options

A. `108p m`
B. `40p m`
C. `127p m`
D. `80p m`

Answer

3

Explanation

Since there are four metal atoms in one unit cell the metal crystalline in `FC C` lattice.For `FC C` unit cell
`4r=sqrt(2)a`
`r=(sqrt(2))/(4)a=(sqrt(2))/(2.2)a=(sqrt(2)a)/(2sqrt(2)sqrt(2))`
`=(a)/(2sqrt(2))`
`=(361p m)/(2sqrt(2))`
`=127p m =(sqrt(2)=1.414)`