Question

Question 107.
(a) Calculate the number of unit cells in 8.1 g of aluminium if it crystallizes in a
f.c.c. structure. (Atomic mass of Al = 27 g mol-1)
------------------------
(b) Give reasons:
(i) In stoichiometric defects, NaCl exhibits Schottky defect and not Frenkel
defect.
(ii) Silicon on doping with Phosphorus form n-type semiconductor.
substances. (Delhi) 2017​

Answer 1

❒ Given :

• → Mass of Al = 8.1
• → Atomic mass of Al = 27 g mol-1
• → No. of atoms = η × 6.022 × 1023

❒ According to Question :

• → 8.127 × 6.022 × 1023
• → 0.3 × 6.022 × 1023
• → 1.8066 × 1023
• → Since one f.c.c. unit cell has 4 atoms
• → ∴ No. of unit cells = 1.8066×10234
• → 4.5 × 1022 unit cells

______________

★ In stoichiometric defects, NaCl exhibits Schottky defect and not Frenkel defect ?

• ⌬ Schottky defect is shown by the ionic solids having very small difference in their cationic and anionic radius whereas Frenkel defect is shown by ionic solids having large difference in their cationic and anionic radius.
• ⌬ NaCl exhibits Schottky defect because radius of both Na+ and Cl– have very small difference.

★ Silicon on doping with Phosphorus form n-type semiconductor substances ?

• ⌬ Phosphorus is pentavalent that is it has 5 valence electrons, an extra electron results in the formation of n-type semi conductorson doping with Silicon.
• ⌬ The conductivity is due to presence of extra electrons.

______________

Answer 2

$\huge\sf \pmb{\orange {\underline\pink{\underline{\: \: Ꭺ ꪀ \mathfrak ꕶ᭙ꫀя \: \: }}}}$

a) $\large\mathscr \purple{ Given: }$

$\longrightarrow$ Mass of Al = 8.1

$\longrightarrow$ Atomic mass of Al = 27g mol-1

$\longrightarrow$ No. of atoms = $\rm n × 6.022 × 1023$

$\large\mathscr \red{ According \: To \: The \: Question: }$

$\longrightarrow$${ 8.127×6.022×1023 }$

$\longrightarrow$${ 0.3×6.022×1023}$

$\longrightarrow$${1.8066×1023}$

$\longrightarrow$ Since one f.c.c. unit cell has 4 atoms.

$\therefore$ No. of unit cells = $1.8066×10234$

$\longrightarrow$ $\rm 4.5×1022 \: unit \: cells$

b) Give reasons:

i) In stoichiometric defects, NaCl exhibits Schottky defect and not Frenkel defect. In NaCl, the cation $\red{ (Na + ) }$ and anion $\red{ (Cl− ) }$ are of almost similar sizes. Whereas Frenkel defect is generally found in ionic crystals where anion is much larger in size then that the cation.

ii) Silicon belongs to group-14 and phosphorus belongs to group-15. On doping, there will be a free electron. Hence, it is n-type semiconductor.

━━━━━━━━━━━━━━━━━━━━