(A) For a $bcc$ unit cell,the relationship between the edge length $(a)$ and the atomic radius $(r)$ is given by the formula: $\sqrt{3} \ a = 4 \ r$.

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(A) For a $bcc$ unit cell,the relationship between the edge length $(a)$ and the atomic radius $(r)$ is given by the formula: $\sqrt{3} \ a = 4 \ r$. Given $a = 4 \times 10^{-10} \ m$. Substituting the value of $a$ in the formula: $r = \frac{\sqrt{3} \times a}{4} = \frac{\sqrt{3} \times 4 \times 10^{-10}}{4} = \sqrt{3} \times 10^{-10} \ m$.

Class 12 Chemistry Solid State Mathematical analysis of cubic system and Bragg’s equation

Medium

The edge length of a $bcc$ unit cell is $4 \times 10^{-10} \ m$. What is the radius of the atom occupying the body center of the cubic unit cell?

A
$\sqrt{3} \times 10^{-10} \ m$
B
$4 \times 10^{-10} \ m$
C
$0.414 \times 4 \times 10^{-10} \ m$
D
None of these

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Mathematical analysis of cubic system and Bragg’s equation

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The edge length of a $bcc$ unit cell is $4 \times 10^{-10} \ m$. What is the radius of the atom occupying the body center of the cubic unit cell?

Similar Questions

How many unit cells are present in $100 \ g$ of an element with $fcc$ crystal structure having density $10 \ g/cm^{3}$ and edge length $100 \ pm$?

Silver forms $ccp$ lattice and $X$-ray studies of its crystals show that the edge length of its unit cell is $408.6 \,pm$. Calculate the density of silver ( Atomic mass $= 107.9 \,u$ ).

Calculate the number of atoms present in $90 \text{ g}$ of a metal that forms a $bcc$ structure. Given: $[\rho \times a^3 = 1.8 \times 10^{-22} \text{ g}]$, where $\rho$ is density and $a$ is the edge length of the unit cell.

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