Question

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

• A. $2.8\times {10}^{25}$
• B. $4.5\times {10}^{22}$
• C. $3.5\times {10}^{24}$
• D. $9.2\times {10}^{24}$

Answer 1

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

Number of atoms in unit cell $=1+2=3$
Volume of unit cell $=24\times {10}^{-24}$ cm${}^3$, density $=7.2$ g cm${}^{-3}$
$\because \text{Density}=\frac{n\times \text{Atomic mass}}{V\times N_a}$
$\therefore 7.2=\frac{3\times \text{Atomic mass}}{24\times {10}^{-24}\times 6.023\times {10}^{23}}$
$\therefore \text{Atomic mass}=34.69$ amu
$\because 34.69$ g has number of atoms $=6.023\times {10}^{23}$
$\therefore 200$ g has number of atoms $=\frac{6.023\times {10}^{23}\times 200}{34.69}$ $=3.4722\times {10}^{24}$ atoms