Question

Potassium has a bcc structure wit nearest neighbour distance $4.52A^0$, its atomic weight is $39$. Its density (in kg $m^{-1}$) will be:

• A. $454$
• B. $804$
• C. $852$
• D. $908$

Answer 1

Answer: (D)

$908$

For b.c.c, $d=\frac{\sqrt{3}a}{2}$

or $a=\frac{2d}{\sqrt{3}}$

$a=\frac{2\times 4.52}{1.732}$

$a=5.219A^{\circ }=522pm$

Hence,

$\rho =\frac{z\times M}{a^3\times N_A\times {10}^{-30}}$

Implies that

$\rho =\frac{2\times 39}{{\left(522\right)}^3\times 6.023\times {10}^{23}\times {10}^{-30}}$

$\rho =0.91g/c{m}^3$

$\rho =910kg{m}^{-3}$