Question

Sodium has a bbc structure with nearest neighbour distance 365.9 pm. Calculate its density(atomic mass of sodium = 23)​

Answer 1

Answer:

Sodium has a bcc strcture with nearest neighbiourneighbour distance 365.9 pm. Caculate its density(Atomic mass of sodium = 23) or a=2√3d=21.732×365.9=422.5 pm.

Answer 2

Answer :

• Density of Sodium = 1.51 g/cm³

Step-by-step explanation :

Given that,

• Atomic mass(M) of sodium = 23.
• Nearest neighbour distance(d) = 365.9 picometer(pm).

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We know, for the bbc structure, nearest neighbour distance(d) is related to the edge length(a) as:-

$\implies\bold{d=\dfrac{\sqrt{3}}{2}a}$

$\implies\bold{a=\dfrac{2}{\sqrt{3}}d}$

$\implies\bold{a=\dfrac{2}{1.732}\times{}365.9}$

$\implies\bold{422.5\:pm}$

Also, for bbc structure, Z = 2

$\therefore\:\bold{\rho=\dfrac{Z\times{}M}{a^3\times{}N_0}}$

$\implies\bold{\dfrac{2\times{}23\:g\:mol^{-1}}{(422.5\times{}10^{-10}\:cm)^3\times{}(6.02\times{}10^{23}\:mol^{-1})}}$

$\implies\bold{1.51\:g/cm^3}$

∴ Density of sodium is 1.51 g/cm³