Question

An element crystallises into a structure which may be described by cubic type of unit cell having one atom on each corner of the cube and two atoms on one of its diagonal. If the volume of this unit cell is $24\times {10}^{-24}c{m}^3$ and density of element in $7.2gc{m}^{-3},$ the number of atoms present in $200g$ of element is:

• A. $3.5\times {10}^{24}$
• B. $5.7\times {10}^{23}$
• C. $6.3\times {10}^{20}$
• D. $1\times {10}^{10}$

Answer 1

The correct option is A $3.5\times {10}^{24}$

In the given crystal structure atoms are present at each corners and two atoms are present on one of the body diagonals.

So, number of atoms in the crystal $=\frac{1}{8}\times 8+2=1+2=3$

Theoretical density of crystal is given by $\rho =\frac{nM}{N_o{a}^3}g/c{m}^3$

$\Rightarrow M=\frac{\rho .N_o.a^3}{n}$

$=\frac{7.2\times 6.022\times {10}^{23}\times 24\times {10}^{-24}}{3}$

$=34.6g$

Number of moles of the given element in $200g=\frac{200}{34.6}=5.8$

Since, $1$ mole of element contains $6.022\times {10}^{23}$ atoms

$\Rightarrow$ Number of atoms in $200g=5.8\times 6.022\times {10}^{23}=3.5\times {10}^{24}$

Hence, Option "A" is the correct answer.