Question

Q. What is the meaning of nearest neighbour? Sodium has BCC structure with nearest neighbour distance 365.9pm. Calculate its density.

Answer 1

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Answer 2

Answer : The density is, $1.559g/Cm^{3}$

Solution :

Nearest neighboring : The number of atoms or ions nearest to the given atoms or ions in the crystal lattice.

Given : Number of atom in unit cell of BCC (Z) = 2

Edge length = $365.9pm=365.9\times 10^{-10}cm$     $(1pm=10^{-10}cm)$

Atomic mass of sodium (M) = 23 g/mole

Avogadro's number $(N_{A})=6.022\times 10^{23} mol^{-1}$

Formula used :  

$\rho=\frac{Z\times M}{N_{A}\times a^{3}}$      .............(1)

where,

$\rho$ = density

Z = number of atom in unit cell

M = atomic mass

$(N_{A})$ = Avogadro's number  

a = edge length of unit cell

Now put all the values in above formula (1), we get

$\rho=\frac{2\times (23g/mol)}{(6.022\times 10^{23}mol^{-1}) \times(365.9\times 10^{-10}Cm)^3}=1.559g/Cm^{3}$

Therefore, the density is, $6.808g/Cm^{3}$