Match the column I with Column II and mark the appropriate choice .

Options

A. A-(iii) , B-(ii), C-(i)
B. A-(i),B-(ii) ,C-(iii)
C. A-(ii),B-(i) , C-(iii)
D. A-(iii) , B-(i) , C-(ii)

Answer

A

Explanation

For simple cubic structure,
`V=a^3` (volume of the unit cell )
`V'=4/3pir^3` (volume of one atom )
`=4/3pi(a/2)^3=(pia^3)/6`
Packing efficiency =`(V')/V=(pia^3//6)/a^3=pi/6`=0.52 or 52%
For fcc structure,
`V'=4xx4/3pir^3`( 4 atoms per unit cell)
`r=a/(2sqrt2)`
`V'=16/3pi(a/(2sqrt2))^3=pi/(3sqrt2)a^3`
Volume of unit cell=`V=a^3`
Packing efficiency =`(V')/V=(pia^3)/(3sqrt2a^3)=pi/(3sqrt2)`=0.74 or 74%
For bcc structure,
`V'=2xx4/3pir^3` (2 atoms per unit cell)
`r=sqrt3/4a`
`V'=2xx4/3pi(sqrt3/4a)^3=(sqrt3pia^3)/8`
`V=a^3`
Packing efficiency =`(V')/V=(sqrt3pia^3)/(8a^3)=sqrt3/8pi`=0.68 or 68%