Question

A mole of a newly discovered crystalline substance weighs 14.56 grams and displaces 2.3 ml of water. Find the atomic radius and density of each atom if it is a simple cubic cell? BCC? FCC? HCP?

Answer 1

V=2.5mL=2.5cm³ =2.5×10^-6 m³

V=L³

2.5×10^-6m³ =L³

L=0.09259×10^-2m

L=9.259×10^-4m

$\therefore$ Atomicradius=$\frac{1}{2}×length$

$\frac{1}{2}$ ×9.259×10^-4

=0.00046295m

=462.95μm

Mass=14.56g=0.01456kg

Volume =2.5×10^-6 m³

$\therefore$ $\rho=\frac{mass}{volume}$

$=0.01456kg\div$ 2.5×10^-6 m³

=5.824×10³kg/m³