Answer any ten questions (All 15 solved for full coverage): 2 x 10 = 20
According to Bohr's theory, the centripetal force is balanced by electrostatic force: (mv²)/r = (Ze²)/(4πε₀r²). Combining this with the quantization of angular momentum, mvr = nh/(2π), we get the expression for radius:
r = (n²h²ε₀) / (πmZe²)
For the first radius of H-atom (n=1, Z=1), the radius is denoted as a₀ (Bohr radius).
From de Broglie's equation, λ = h / (mv). Since velocity (v) and h are constants, wavelength (λ) is inversely proportional to mass (m). Because the mass of a proton is significantly higher than that of an electron, the electron will have a much longer wavelength than the proton.
The nitrate ion has three equivalent resonance structures where a double bond is shared among the three oxygen atoms, resulting in a formal charge of -1.
The law states that if two or more substances have the same reduced pressure and reduced temperature, they will also have the same reduced volume.
Surface tension decreases as temperature increases. This is because higher kinetic energy at elevated temperatures weakens the intermolecular attractive forces between liquid molecules.
A lattice point represents the position of a constituent particle (atom, ion, or molecule) in a crystal. The collection of these points defines the geometry of the crystal lattice.
The Ostwald Viscometer method is commonly used. It measures the time taken for a fixed volume of liquid to flow through a capillary under gravity. The viscosity is determined relative to a reference liquid (usually water) using the formula: η₁/η₂ = (d₁t₁)/(d₂t₂).
Inductive effect is the permanent displacement of shared sigma (σ) electrons along a carbon chain due to the presence of an atom or group with different electronegativity.
(i) CH₂=CH-CH₂⁻ (Allyl carbanion) is the most stable.
This is because the negative charge is delocalized over two carbon atoms through resonance, whereas (ii) and (iii) lack such stabilization.Answer any five questions: 10 x 5 = 50
(a) Schrödinger Equation: ∇²ψ + (8π²m/h²)(E - V)ψ = 0.
ψ is the wave function, E is total energy, V is potential energy, m is mass, and h is Planck's constant.(b) Orbital Designations: (i) n=2, l=1 is 2p; (ii) n=3, l=2 is 3d.
(c) Heisenberg's Uncertainty Principle: It is impossible to determine simultaneously and precisely both the position and momentum of a microscopic particle: Δx · Δp ≥ h / 4π.
(d) Velocity Calculation: Using v = h / (mλ). Given m = 9.11×10⁻³¹ kg, λ = 7.27 Å = 7.27×10⁻¹⁰ m.
(a) VBT Postulates: Covalent bonds form by the overlap of half-filled atomic orbitals; the strength depends on the extent of overlap; orbitals must have similar energy and symmetry.
(b) [FeF₆]³⁻: Fe³⁺ has a 3d⁵ configuration. Since F⁻ is a weak field ligand, no pairing occurs. There are 5 unpaired electrons, leading to a spin-only magnetic moment of √[5(5+2)] = 5.92 BM.
(c) Significance of ψ and ψ²: ψ is the amplitude of the wave; ψ² represents the probability density of finding an electron at a specific point in space.
(c) O₂ Molecule: Configuration (16e⁻): σ1s² σ*1s² σ2s² σ*2s² σ2pz² π2px²=π2py² π*2px¹=π*2py¹.
Bond Order = (10 - 6) / 2 = 2. It is paramagnetic due to 2 unpaired electrons in π* orbitals.(c) CO Molecule: BO is 3 (triple bond) and it is diamagnetic as all electrons are paired.
(a) van der Waals' Equation: (P + an²/V²)(V - nb) = nRT.
(c) Velocity Expressions:
(b) Schottky vs Frenkel Defects:
(c) Atoms per Unit Cell in Cubic Systems:
(a) Bond Fission: Homolytic fission of CH₃-Cl gives CH₃· and Cl· (free radicals).
Heterolytic fission gives CH₃⁺ and Cl⁻ (ions).(b) Carbocations: Carbon species with a positive charge and 6 valence electrons.
They are sp² hybridized with trigonal planar shape. Stability order: 3° > 2° > 1° > Methyl.(c) Free Radicals: Neutral species with an unpaired electron.
Stability follows the same order as carbocations due to hyperconjugation.