Question

What is the density of potassium, if it has bcc structure with edge length $4 \mathring{A}$ ? (Atomic mass of $K=39$ )

• A. $3\, g\, cm ^{-3}$
• B. $2 \, g\, cm ^{-3}$
• C. $5\, g\, cm ^{-3}$
• D. $4\, g\, cm ^{-3}$

Answer 1

Answer: (B)

For density, $\rho=\frac{z \times M}{a^3 \times N_A}$
Edge length, $a=4 \mathring{A}=4 \times 10^{-8} cm$
For bcc structure, $Z=2$
$\rho =\frac{2 \times 39}{\left(4 \times 10^{-8}\right)^3 \times 6.022 \times 10^{23}}$
$ =0.202 \times 10^{24} \times 10^{-23} g\,cm ^{-3} $
$=0.202 \times 10 gcm ^{-3}=2.02\, g\,cm ^{-3}$