Question

An elemental crystal has a density of $8570 \,kg / m ^{3}$. The packing efficiency is $0.68$. The closest distance of approach between neighbouring atom is $2.86 \,?$. What is the mass of one atom approximately?

• A. 93 amu
• B. 39 amu
• C. 63 amu
• D. 29 amu

Answer 1

Answer: (A)

93 amu

Answer 2

The packing efficiency $= 0.68$, means the given lattice is BCC.
The closest distance of approach $= 2r$
$2r = 2.86\, ? = a \sqrt{3}$
or $a = \frac{ 2 \times 2.86}{\sqrt{3}} = 3.30\,?$
Let atomic weight of the element $= a$
$\therefore \frac{2 \times9}{36 \times10^{23} \times\left(3.3\right)^{3} \times10^{-24}} = 8.57$
$a = 8.57 \times 3 \times \left(3.3\right)^{3} \times 0.1$
$= 92.39 \simeq 93$ amu