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

  • Option 1)

    \frac{2}{\sqrt{3}}\text{a}

  • Option 2)

    \frac{4}{\sqrt{3}}\text{a}

  • Option 3)

    \frac{\sqrt{3}}{4}\text{a}

  • Option 4)

    \frac{\sqrt{3}}{2}\text{a}

 

Answers (1)

As we learnt in 

z for body centered unit cell -

Lattice points: at corners and body center of unit cell.

For body centered cubic (BCC), z=2

- wherein

 

In a bcc lattice, we have an atom  at the center and distance between it and the corner atom will be  

\sqrt{\left ( \frac{\sqrt{2}}{2} \right )^{2}+\left ( \frac{1}{2} \right )^{2}} a=\frac{\sqrt{3}}{2}a


Option 1)

\frac{2}{\sqrt{3}}\text{a}

Incorrect

Option 2)

\frac{4}{\sqrt{3}}\text{a}

Incorrect

Option 3)

\frac{\sqrt{3}}{4}\text{a}

Incorrect

Option 4)

\frac{\sqrt{3}}{2}\text{a}

Correct

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