Question

An element with body centred structure has cell edge 400pm .Calculate the density of the element? (Atomic number-100)

Answer 1

The element has body centered structure so the unit cell contains 2 atoms.

• $\sf{Z=2}$

The unit cell edge has length 400 pm.

• $\sf{a=400\ pm=4\times10^{-8}\ cm}$

Atomic mass of the element,

• $\sf{M=100\ g\,mol^{-1}}$

Then density of the element is given by,

$\longrightarrow\sf{\rho=\dfrac{Z\,M}{a^3\,N_A}}$

where $\sf{N_A}$ is Avogadro Number.

$\longrightarrow\sf{\rho=\dfrac{2\times100}{(4\times10^{-8})^3\,\times6.022\times10^{23}}}$

$\longrightarrow\underline{\underline{\sf{\rho=5.189\ g\ cm^{-3}}}}$