Question

An element has a body centred cubic structure with a cell edge of $288$pm. The density of the element is $7.2gc{m}^3$. How many atoms are present in $208$g of the element?

Answer 1

Solution -

For bcc geometry, no of

atoms per unit cell $\left(z\right)=2$

Edge length $\left(a\right)=288\times {10}^{-10}cm$

Density $=7.2g/c{m}^3$

Atomic mass = ?

we know that,

Density $=\frac{Z\times M}{N\times a^3}$

$\Rightarrow 7.2=\frac{2\times M}{(6.02\times {10}^{23})\times (288\times {10}^{-10}{)}^3}$

$\Rightarrow 7.2=\frac{2\times M}{6.02\times 2.38}$

$\Rightarrow 51.58=M$

No. of moles $=\frac{mass}{molarmass}$

$\Rightarrow \frac{208}{51.58}=4.03$

No.of atoms $\Rightarrow 4.03\times 6.02\times {10}^{23}$

$\Rightarrow 24.2\times {10}^{23}atoms$