Percentage of free space in cubic in a body- centred cubic unit cell is .

Options

A. `30%`
B. `32%`
C. `34%`
D. `28%`

Answer

B

Explanation

In bcc unit cell, the number of atoms = 2
Thus, volume of atoms in unit cell `(v)=2xx(4)/(3)pir^(3)`
For bcc structure`(r)=(sqrt3)/(4)a`
`(V)=2xx(4)/(3)pi((sqrt3)/(4)a)^(3)=(sqrt3)/(8)pia^(3)`
Volume of unit cell `(V)=a^(3)`
Percentage of volume occupied by unit cell
`("Volume of the atoms in unit cell")/("Volume of unit cell")`
`=((sqrt3)/(8)pia^(3))/(a^(3))xx100=(sqrt3)/(8)pixx100=68%`
Hence, the free space in bcc unit cell `=100-68`
`=32%`