Question

An element has a body centered cubic structure with a cell edge length of 288 pm. The density of dement is 7.2 g/cm${}^3$. How many atoms are present in 100 g of this element?

Answer 1

$\rho =\frac{Z\times M_A}{N_A\times a^3}$

$\rho =7.2$ $g/c{m}^3$

$Z=2$(for body centered)

$a=288$ $pm$

$M_A=?$

$7.2=\frac{2\times M_A}{6.023\times {10}^{23}\times 23.88\times {10}^{-24}}$

$M_A=51.7$

Number of atoms $=\frac{100}{51.7}\times 6.023\times {10}^{23}$ $(Moles\times N_A)$

$=1.65\times {10}^{24}$ atoms