An element crystallizes into a structure which may be described by a cubic type of unit cell having one atom on each corner of the cube and two atoms on one of its diagonals. If volume of this unit cell is 24 × 10^-24 cm³ and density of the element is 7.2 g/cm³, the number of atoms present in 200 g of the element is $3.4\times {10}^a$, the value of a is

Given that, total number of atoms per unit cell,

Z =  1 + 2  = 3 atoms

$\text{ Volume of unit cell }=24\times {10}^{-24}{\mathrm{cm}}^3$

Density of the element = 7.2 g/cm³

$\text{ We know, density, }\rho =\frac{Z\times \text{ Atomic mass }}{N_{\mathrm{A}}\times \text{ Volume of unit cell }}$

$\text{ or atomic mass }=\frac{\rho \times N_A\times \text{ Volume of unit cell }}{Z}$

since $346.9\mathrm{g}\text{ of element contains }=6.023\times {10}^{23}\text{ atoms }$

$\therefore$ 200 g of element contains

$=\frac{6.023\times {10}^{23}\times 200}{346.9}=3.47\times {10}^{23}\text{ atoms }$