Q. Potassium has a $bcc$ structure with nearest neighbor distance $4.525\ \mathring{\mathrm{A}}$. Its molecular weight is 39. Its density in $kg/m^{3}$ is

A) 900
B) 494
C) 602
D) 802
Explanation

(a) Density $\rho = \frac{nA}{N(a)^{3}}$
where $n = 2$ for bcc structure, $A = 39 \times 10^{- 3}kg$
$N = 6.02 \times 10^{23},\ a = \frac{2}{\sqrt{3}}d = \frac{2}{\sqrt{3}} \times \left( 4.525 \times 10^{- 10} \right)m$
$\lbrack d =$ nearest neighbor distance $=$ distance between centres of two neighbouring atoms $= \frac{\sqrt{3}}{2}a\rbrack$
On putting the values we get $\rho = 907$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.