Question

Potassium has a bcc structure with nearest neighbor distance $4.53A$. Its atomic weight is 39. Its density will be:

• A. $454kg{m}^{-3}$
• B. $804kg{m}^{-3}$
• C. $852kg{m}^{-3}$
• D. $908kg{m}^{-3}$

Answer 1

Answer: (D)

$908kg{m}^{-3}$

Nearest distance in BCC structure is $\frac{a\sqrt{3}}{2}$ along the body diagonal connecting body centre to the body corners.

$\frac{a\sqrt{3}}{2}=4.53$

$\Rightarrow a=5.23\mathring{A}$

$Z=2$ (for BCC)

$M_A=39$

$N_A=6.023\times {10}^{23}$

$\rho =\frac{Z\times M_A}{N_A\times a^3}=\frac{2\times 39}{6.023\times {10}^{23}\times 143\times {10}^{-24}}$

$\rho =0.908$ $g/c{m}^3$

In S.I units $\rho =908$ $kg/m^3$