Nuclear and Solid State Chemistry

For 17280 years, the number of half-life (n) = 3
Cⁿ = (1/2)ⁿ= (1/2)³ = 1/8
1/8 of 200 mg = 25 mg
So, after 17280 years, the amount of C-14 in the sample will be reduced to 25 mg.

Half-life = 30 minutes
For 2 hrs, the number of half-life (n) = 4
Cn = 1/2ⁿ= 1/2⁴ = 1/16 = 6.25%
So, after 2 hrs the amount of radioactive substance will be reduced to 1/16th (6.25%) of its initial amount.
Hence, the amount decayed during 2 hrs = (100 - 6.25)% = 92.75%

₉₂U²³⁸ → ₈₂Pb²⁰⁶
Change in mass number = 238 - 206 = 32
The mass number changes only because of α-particle emission
Hence, number of α-particles emitted = 32/4 = 8
After emission of 8 α-particles, the atomic number should change by 2 x 8 = 16
Actual change in atomic number = 92 - 82 = 10
Hence, number of β-particles emitted = 16 - 10 = 6

₉₀Th²³² → ₈₈Ra²²⁸ + ₂He⁴(α-emission)
₈₄Po²¹⁰ → ₈₂Pb²⁰⁶ + ₂He⁴(α-emission)

Crystal system with edge length a ≠ b ≠ c, and axial angles α = β = γ = 90° is an orthorhombic crystal system.

₉₂X²³⁸ → ₈₈Y²¹⁸
Change in mass number = 238 - 218 = 20
The mass number changes only because of α-particle emission
Hence, number of α-particles emitted = 20/4 = 5
After emission of 5 α-particles, the atomic number should change by 2 x 5 = 10
Actual change in atomic number = 92 - 88 = 4
Hence, number of β-particles emitted = 10 – 4 = 6
After emission of 5 α and 6β particles from ₉₂X²³⁸, product formed is ₈₈Y²¹⁸.
Atomic number of product = 88
Mass number of product = 218

₁₃Al²⁷ (α, p) ₁₅P³⁰ (Incorrect notion)
Correct product is ₁₄Si³⁰.
₁₃Al²⁷ + ₂He⁴ → ₁₄Si³⁰ + ₁H¹

Correct option; Except 1, 3, and 4, rest are incorrect statements.
A fully occupied band separated from the next (empty) band by a large energy separation (the band gap) leads to the material being an insulator.
A band gap occurs when there is some energy difference between two bands.
Electrical conductivity is a characteristic property of partially filled bands of MOs.
Overlapping of both bands leads to the material being metallic.
Large energy gap between bands leads to the material being an insulator.

Metal deficiency defect are generally found in NiO.

Substances like MnO showing antiferromagnetism have a domain structure similar to ferromagnetic substance, but their domains are oppositely oriented and cancel out each other's magnetic moment

Intrinsic semiconductors are semiconductors due to thermal defects. At 0K, pure Si or Ge act as insulators, however at higher temperatures, some of the covalent bonds are broken and the electrons so released become free to move in the crystal and thus conduct electricity.
Extrinsic semiconductors are semiconductors due to impurity defects. Si and Ge (group 14 elements) in pure state have very low electrical conductivity. Their electrical conductivity can be enhanced by the addition of traces of elements belonging to group 13 and 15. Introduction of group 13 or 15 elements to the crystal lattice of group 14 elements p-type and n-type semiconductors respectively. The process of adding impurities is called doping.

Frenkel defect leads to no change in density but Schottky leads to decrease in density. N-type semiconductor is the result of doping of group 15 into group 14.

Crystal systems are differentiated on the basis of their edge lengths and axial angles. So, option 2 classifies them on this basis.
Monoclinic - a ≠ b ≠ c, α = γ = 90°, β ≠ 90°
Tetragonal - a = b ≠ c, α = β = γ = 90°
Orthorhombic - a ≠ b ≠ c, α = β = γ = 90°
Trigonal - a = b = c, α = β = γ ≠ 90°

₉₂U²³⁵ + ₀n¹ → ₅₆Ba¹⁴⁴ + ₃₆Kr⁸⁹ + 3 ₀n¹ +210 MeV
Nuclear fission reaction

Correct answer.
MgAl₂O₄ crystallizes to form spinel structure.
FeTiO₃ crystallizes to form ilmenite structure.
CaTiO₃ crystallizes to form perovskite structure.
TiO₂ crystallizes to form rutile structure.