Question

Aluminium molecular weight 27 crystallises in a cubic unit cell with the edge length a=100pm with density d=180g/cm^3 then type of unit cell is

Answer 1

Answer : The type of unit cell is FCC (Face centered cubic).

Solution : Given,

Molecular weight of Aluminium  = 27 g/mole

Edge length of unit cell = 100 pm = 100 × $10^{-10}$ Cm = $10^{-8}$ Cm

Conversion :   1 pm = $10^{-10}$ Cm

Density = 180 $g/Cm^{3}$

Avogadro's number = 6.022 × $10^{23}$ $mol^{-1}$

Formula used :

$\rho=\frac{Z\times M}{N_{A}\times a^{3}}$

where,

$\rho$ = Density

Z = type of unit cell or number of unit cell in an atom

M = Molecular weight

$N_{A}$ = Avogadro's number

a = Edge length of unit cell

Rearranging the above formula, we get

$Z=\frac{\rho \times N_{A}\times a^{3}}{M}$

Now put all the given values in this formula, we get

$Z=\frac{(180g/Cm^{3}) \times (6.022\times 10^{23}mol^{-1})\times (10^{-8}Cm)^{3}}{27g/mole}$ = 4.01466 $\approx$ 4

The value of Z = 4. The image is also shown below.

Therefore, the type of unit cell is FCC (Face centered cubic).

Answer 2

Answer:

Explanation:hope this helps u