A metal crystallizes in `bcc` lattice. The percent fraction of edge length not covered by atom is

Options

A. `12.4%`
B. `13.4%`
C. `87.6%`
D. `50.0%`

Answer

B

Explanation

In bcc, radius of atom,
`r = (sqrt(3)alpha)/(4)`
where a is the edge length
The edge length not covered by atoms = `a - 2r`
`= a - 2 xx (sqrt3)/4 a = a ((2 - sqrt(3))/(2))`
`= (a(2 - 1.732))/(2) = 0.134 a`
Percentage of edge length not covered
`= (0.134 a)/a xx 100 = 13.4 %. `