The radius of the largest shpere which fits properly at the centre of the edge of a body centred cubic unit cell is : (Edge length is represented by 'a')

Options

A. `0.134 a`
B. `0.027 a `
C. `0.067 a`
D. `0.047 a`

Answer

C

Explanation

`a = 2(R + r)`
`a/2 = R + r " " …..(i)`
In a body centred cubic unit cell
`sqrt(3)a = 4R`
Or `R = (sqrt(3)a)/(4)`
Substituting in eq. (i)
`a/2 = (sqrt(3)a)/(4) + r`
or `r = a/2 - (sqrt(3)a)/(4) = a((2 - sqrt(3))/(4))`
`= (a(2 - 1.732))/(4) = 0.067 a`.