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Consider a cube 1 of Body Centered Cubic...

Consider a cube 1 of Body Centered Cubic unit cell of edge length a now atom at the body center can be viewed to be lying on the corner of another cube2. Find the volume common to cube 1 and cube 2

A

`(a^(3))/(27)`

B

`(a^(3))/(64)`

C

`(a^(3))/(2sqrt2)`

D

`(a^(3))/(8)`

Text Solution

Verified by Experts

The correct Answer is:
D
Common volume `= ((a)/(2))^(3) = (a^(3))/(8)` [`:.` common vol is a cube of edge length `(a)/(2)`]
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Knowledge Check

  • if a is the length of the side of a cube, the distance between the body-centred atom and one corner atom in the cube will be

    A
    `2sqrt3a`
    B
    `4/sqrt3a`
    C
    `sqrt3/4a`
    D
    `sqrt3/2 a`

  • If a is the length of the side of a cube, the distance between the body-centred atom and one corner atom in the cube will be

    A
    `2/sqrt3 a`
    B
    `4/sqrt3 a`
    C
    `sqrt3/4 a`
    D
    `sqrt3/2 a`

  • If a is the length of the side of a cube, the distance between the body centred atom and one corner atom in the cube will be:

    A
    `(2)/(sqrt(3))a`
    B
    `(4)/(sqrt(3))r`
    C
    `(sqrt(3))/(4)a`
    D
    `(sqrt(3))/(2)a`