The Solid State

Question 233

Calculate the efficiency (percentage of volume occupied and unoccupied) of packing in case of a metal crystal for simple cubic.


Let ‘a’ be the edge length of the unit cell and r be the radius of sphere.

As sphere are touching each other

Therefore a = 2r

No. of spheres per unit cell = 1/8 × 8 = 1 

Volume of the sphere = 4/3 πr3 

Volume of the cube = a3= (2r)3 = 8r3

∴ Fraction of the space occupied = 1/3πr3 / 8r3 = 0.524

∴ % occupied = 52.4 %

Question 234

 (a) Determine the type of cubic lattice to which a given crystal belongs if it has edge length of 290 pm and density is 7.80 g cm–3. (Molecular mass.= 56 g mol–1)

(b) Why does zinc oxide exhibit enhanced electrical conductivity on heating?


we know that

d =ZMa3NA

as we have given 
d= 7.80 g cm–3.
M=56 g mol–1
a= 290 pm or a3 =2.43 x10-23
putting all value in above equation we get,

Z =a3 x d xNAMZ= 2.43 x10-23 x 7.80 x6.022 x102356 =2.03

hence it belong to bcc crystal lattice.

b) Zinc oxide is white in colour at room temperature. On heating it loses electron and turns yellow in colour. 

ZnO Zn2+ +12O2 +2e- 

The electron liberate after heating, can act as charge carrier and thus on heating zinc oxide it exhibit electrical conductivity.

Question 235

The compound CuCl has the ZnS (Cubic) structure. Its density is 3.04 g cm–3. What is the length of the edge of unit cell? (At. mass of Cu = 63.5, CI = 35.5) 


Formula mass of CuCl =63.5 +35.5

                                      =  99.0

The number of formula units per cell of ZnS is 4. It has face centred cubic structure.

 we have Z  =4density (d) =3.4 g Cm-3N0 (Avogadro's number) =6.023 x1023Mass =99.0 gramTherefore using formula density =Mass x Zunit cell volume(Cm)3 =M x Za3 x N0a3 =99 x43.4 x6.023 x1023a3 =1.932 x10-22cm3unit cell length a= (1.932 x10-22)13takinig log both sidelog a =13log  1.932 x10-22       =13(0.2860-22) =13(-21.7140)       = -7.238 =0.762 x10-8taking antilog a =antilog 0.762 x10-8 =5.758 x10-8 cm = 5.758 x 10-8cm

Question 236

Potassium crystallises in a simple cubic unit cell. It has an atomic mass of 209 and its density is 91.5 g m–3. What is the edge length of its unit cell? 


we have given,
Mass= 209 g
Number of  atom per unit cell =1 (Simple cubic)
density =91.5 g m-3
NA =6.023 x1023
edge length of unit cell =?
By applying formula

density = Mass x Number of atom per unit cellvolume of unit cell  x avogadro's numberd= M x Za3 x NA91.5 = 209 x 1a3 x 6.023 x 1023a3 =209 x 191.5 x 6.023 x 1023

a= 15.59 x10-8 cm

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