Question

An element having Bcc geometry has atomic mass 50u. calculate density of unit cell, if it's edge length is 290pm?​

Answer 1

Answer :

Type of unit cell : BCC

Atomic weight = 50u

Edge length = 290pm

We have to find density of unit cell$.$

★ Calculations involving unit cell dimensions :

$\dag\:\:\boxed{\bf{d=\dfrac{Z\times M}{a^3\times N_A \times 10^{-30}}}}$

• Z denotes no. of atoms per unit cell
• a denotes edge length in pm
• d denotes density
• M denotes molar mass
• N_A denotes avogadro's number

★ No. of atoms in unit cell :

• Simple = 1
• BCC = 2
• FCC = 4

By substituting the given values, we get

$\leadsto\sf\:d=\dfrac{Z\times M}{a^3\times N_A \times 10^{-30}}$

$\leadsto\sf\:d=\dfrac{2\times 50}{(290)^3\times (6.022\times 10^{23})\times 10^{-30}}$

$\leadsto\sf\:d=\dfrac{10^2}{14.68}$

$\leadsto\bf\:d=6.81\:g cm^{-3}$