Ratio of the total volume of bcc to simple cubic structure is

Options

A. `3sqrt3:8`
B. `8:3sqrt3`
C. `24sqrt3:1`
D. `1:24sqrt3`

Answer

B

Explanation

Volume of unit cell `= a^3`
For bcc, `r= sqrt3/4 a or a = (4r)/sqrt3`
For simple cubic, `r= a/2 or a = 2r`
Thus volume of simple cubic unit cell = `(2r)^3 = 8r^3`
`("Volume of bcc unit cell")/("Volume of simple cubic") = (64//3sqrt3r^3)/(8r^3) = 64/(8xx3sqrt3) = 8/(3sqrt3)`