Question

Tungsten has atomic radius of 0.136 nm. The density of tungsten is 19.4 g/cm3. What is the crystal structure of tungsten?

Answer 1

Answer : The crystal structure of tungsten is, BCC (Z=2)

Explanation :

Nearest neighbor distance, r = $0.136nm=1.36\times 10^{-8}cm$ $(1nm=10^{-7}cm)$

Atomic mass of tungsten (M) = 184 g/mole

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

First we have to calculate the cubing of edge length of unit cell for SCC, BCC and FCC crystal lattice.

For SCC lattice : $a^3=(2r)^3=(2\times 1.36\times 10^{-8}cm)^3=2.01\times 10^{-23}cm^3$

For BCC lattice : $a^3=(\frac{4r}{\sqrt{3}})^3=(\frac{4\times 1.36\times 10^{-8}cm}{\sqrt{3}})^3=3.09\times 10^{-23}cm^3$

For FCC lattice : $a^3=(\sqrt{8}r)^3=(\sqrt{8}\times 1.36\times 10^{-8}cm)^3=5.69\times 10^{-23}cm^3$

Now we have to calculate the density of unit cell for SCC, BCC and FCC crystal lattice.

Formula used :  

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

where,

$\rho$ = density

Z = number of atom in unit cell  (for SCC = 1, for BCC = 2, for FCC = 4)

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

$\rho=\frac{1\times (184g/mol)}{(6.022\times 10^{23}mol^{-1}) \times (2.01\times 10^{-23}Cm^3)}=15.20g/Cm^{3}$

$\rho=\frac{2\times (184g/mol)}{(6.022\times 10^{23}mol^{-1}) \times (3.09\times 10^{-23}Cm^3)}=19.77g/Cm^{3}$

$\rho=\frac{4\times (184g/mol)}{(6.022\times 10^{23}mol^{-1}) \times (5.69\times 10^{-23}Cm^3)}=21.47g/Cm^{3}$

From this information we conclude that, the given density is approximately equal to the density of BCC unit lattice.

So, the crystal structure of tungsten is, BCC (Z=2)

Answer 2

Dear Student,

◆ Answer -

Body centred cubic crystal structure

● Explanation -

# Given -

d = 19.4 g/cm^3

a = 0.136 nm = 1.36×10^-8 cm

M = 184 g/mol

# Solution -

Density of the solid is given by -

d = Z.M / NA.a^3

Z = d × NA × a^3 / M

Z = 19.4 × 6.022×10^23 × (1.36×10^-8)^3 / 184

Z = 2

We know Z = 2 for BCC. Therefore, Tungsten shows body centred cubic crystal structure.

Thanks for asking..