The packing efficiency of simple cubic (sc.) body centred cubic (bcc) and cubic close packing (ccp) lattices follow the order

Options

A. `bcc lt ccp lt sc`
B. `ccp lt bcc lt sc`
C. `sc lt ccp lt bcc`
D. `sc lt bcc lt ccp`

Answer

D

Explanation

For simple cubic packing efficieny is `((4 pi r^3)/(3))/(a^3)=((4pir^3)/(3))/(8r^3)=((4xx3.142)/(3))/(8)xx100`
`=(4.189)/(8)xx100`
`=52.4%`.
For body cenered cubics
`=(2xx(4)/(3)pir^3)/((64r^3)/(3sqrt(3)))xx100`
`=(2xx(4)/(3)xx3.142)/((64)/(3sqrt(3)))xx100`
`=68%`
For cubic closed packing
`=(4xx 4pi r^3//3)/(32 r^3//sqrt(2))xx100=74%`
`sc lt b c c lt cp`.