Class 11 Chemistry Notes Chapter 2 (Chapter 2) – Examplar Problems (English) Book

Detailed Notes with MCQs of Chapter 2: Structure of Atom from the NCERT Exemplar. This chapter is fundamental for understanding chemistry and frequently tested in various government exams. We'll break down the key concepts systematically.

Chapter 2: Structure of Atom - Detailed Notes for Government Exams

1. Discovery of Fundamental Particles & Early Models

• Electron (e⁻):
  • Discovered via Cathode Ray Discharge Tube experiments (J.J. Thomson).
  • Cathode rays travel from cathode to anode, are negatively charged, deflected by electric/magnetic fields, possess kinetic energy, and produce X-rays when striking heavy metals.
  • Charge-to-mass ratio (e/m_e): Determined by Thomson as 1.758820 × 10¹¹ C kg⁻¹ (constant regardless of gas or cathode material).
  • Charge (e): Determined by R.A. Millikan's Oil Drop experiment as -1.6022 × 10⁻¹⁹ C.
  • Mass (m_e): Calculated from e and e/m_e ratio = 9.1094 × 10⁻³¹ kg (negligible compared to proton/neutron).
• Proton (p⁺):
  • Discovered via modified cathode ray tubes showing Canal Rays/Anode Rays (Goldstein).
  • Positively charged particles originating from the ionization of gas in the tube.
  • e/m ratio depends on the gas used (highest for Hydrogen).
  • Charge: +1.6022 × 10⁻¹⁹ C.
  • Mass (m_p): 1.6726 × 10⁻²⁷ kg (approx. 1837 times heavier than electron).
• Neutron (n⁰):
  • Discovered by James Chadwick by bombarding Beryllium (Be) with α-particles.
  • Electrically neutral.
  • Mass (m_n): 1.6749 × 10⁻²⁷ kg (slightly heavier than proton).
• Thomson's Model (Plum Pudding Model): Atom is a sphere of positive charge with electrons embedded in it. Failed to explain scattering experiments.
• Rutherford's Nuclear Model:
  • Based on α-particle scattering experiment on thin gold foil.
  • Observations: Most α-particles passed straight, some deflected by small angles, very few (1 in 20,000) deflected by >90° or bounced back (180°).
  • Conclusions:
    • Most space in an atom is empty.
    • Positive charge and most mass are concentrated in a very small volume called the nucleus.
    • Electrons revolve around the nucleus like planets around the sun.
  • Drawbacks: Couldn't explain the stability of the atom (accelerating electrons should radiate energy and spiral into the nucleus) or the line spectra of atoms.

2. Atomic Number, Mass Number, Isotopes & Isobars

• Atomic Number (Z): Number of protons in the nucleus (also equals the number of electrons in a neutral atom). Defines the element.
• Mass Number (A): Total number of protons and neutrons in the nucleus (A = Z + number of neutrons). Nucleons = protons + neutrons.
• Representation: ᴬ<0xE2><0x82><0x9 Z>X (e.g., ¹²₆C)
• Isotopes: Atoms of the same element (same Z) but different mass numbers (different number of neutrons). E.g., ¹H (Protium), ²H (Deuterium), ³H (Tritium); ¹²C, ¹³C, ¹⁴C. Have similar chemical properties.
• Isobars: Atoms of different elements (different Z) but the same mass number (A). E.g., ⁴⁰₁₈Ar, ⁴⁰₁₉K, ⁴⁰₂₀Ca. Have different chemical properties.
• Isotones: Atoms of different elements having the same number of neutrons (A-Z is same). E.g., ¹⁴₆C, ¹⁵₇N, ¹⁶₈O (all have 8 neutrons).
• Isoelectronic Species: Atoms or ions having the same number of electrons. E.g., N³⁻, O²⁻, F⁻, Ne, Na⁺, Mg²⁺, Al³⁺ (all have 10 electrons).

3. Developments Leading to Bohr's Model

• Wave Nature of Electromagnetic Radiation (EMR):
  • Oscillating electric and magnetic fields perpendicular to each other and the direction of propagation.
  • Characterized by:
    • Wavelength (λ): Distance between two consecutive crests or troughs (units: m, cm, nm, Å).
    • Frequency (ν): Number of waves passing a point per second (units: Hz or s⁻¹).
    • Velocity (c): Speed of light in vacuum = 3 × 10⁸ m/s. c = νλ
    • Wave Number (ν̄): Number of wavelengths per unit length (ν̄ = 1/λ). Units: m⁻¹, cm⁻¹.
  • Electromagnetic Spectrum: Arrangement of EMR in order of increasing wavelength (or decreasing frequency/energy): Cosmic rays < γ-rays < X-rays < UV < Visible < IR < Microwaves < Radio waves. (Visible: VIBGYOR, ~400 nm to ~750 nm).
• Particle Nature of EMR: Planck's Quantum Theory:
  • Energy is emitted or absorbed discontinuously in small packets called quanta (plural of quantum). In case of light, the quantum of energy is called a photon.
  • Energy of a quantum (E) is proportional to the frequency (ν): E = hν, where h is Planck's constant (6.626 × 10⁻³⁴ J s).
  • Also, E = hc/λ = hcν̄.
  • Black-Body Radiation: An ideal body that emits and absorbs all frequencies. The distribution of intensity vs. wavelength couldn't be explained by wave theory but was explained by Planck's quantum theory.
  • Photoelectric Effect: Ejection of electrons from a metal surface when light of suitable frequency strikes it.
    • Threshold Frequency (ν₀): Minimum frequency required to eject electrons.
    • Work Function (W₀ or Φ): Minimum energy required to eject an electron (W₀ = hν₀).
    • Einstein's Explanation: Light consists of photons (E=hν). When a photon strikes, its energy is used partly as work function and the rest as Kinetic Energy (K.E.) of the ejected electron.
    • K.E. = hν - hν₀ = h(ν - ν₀) or ½ m_e v² = hν - W₀.
    • K.E. depends on frequency (ν), not intensity. Number of electrons ejected depends on the intensity of light.
• Atomic Spectra:
  • Emission Spectrum: Spectrum produced when radiation emitted by a substance (after excitation) is analyzed. Contains bright lines on a dark background (Line Spectrum for atoms).
  • Absorption Spectrum: Spectrum obtained when light is passed through a substance, which absorbs certain wavelengths. Contains dark lines on a bright background.
  • Line Spectrum of Hydrogen: Specific discrete lines observed, indicating quantized energy levels.
    • Rydberg Formula: Predicts the wave number (ν̄) or wavelength (λ) of lines in the hydrogen spectrum:
      ν̄ = 1/λ = R_H Z² (1/n₁² - 1/n₂²)
      Where:
      R_H = Rydberg constant = 109677 cm⁻¹
      Z = Atomic number (Z=1 for H)
      n₁ and n₂ are integers (n₂ > n₁) representing energy levels.
    • Spectral Series:
      • Lyman (n₁=1, n₂=2,3..): UV region
      • Balmer (n₁=2, n₂=3,4..): Visible region
      • Paschen (n₁=3, n₂=4,5..): IR region
      • Brackett (n₁=4, n₂=5,6..): IR region
      • Pfund (n₁=5, n₂=6,7..): Far IR region

4. Bohr's Model for Hydrogen Atom (and H-like species like He⁺, Li²⁺)

• Postulates:
  1. Electrons revolve around the nucleus in specific circular paths called orbits or stationary states, which have fixed energy.
  2. Energy is emitted or absorbed only when an electron jumps from one orbit to another. ΔE = E₂ - E₁ = hν.
  3. The angular momentum of an electron in an orbit is quantized: mvr = n(h/2π), where n = 1, 2, 3... (Principal Quantum Number).
• Results:
  • Radius of nᵗʰ orbit (r_n): r_n = (0.529 Å) × n²/Z
  • Energy of nᵗʰ orbit (E_n): E_n = -2.18 × 10⁻¹⁸ J × Z²/n² = -13.6 eV × Z²/n²
  • Successfully explained the hydrogen spectrum and stability.
• Limitations:
  • Failed for multi-electron atoms.
  • Couldn't explain the fine structure of spectral lines.
  • Couldn't explain splitting of spectral lines in magnetic field (Zeeman effect) or electric field (Stark effect).
  • Couldn't explain the ability of atoms to form molecules (chemical bonding).
  • Violated Heisenberg's Uncertainty Principle (fixed orbits imply definite position and momentum).
  • Did not consider the dual nature of matter.

5. Towards Quantum Mechanical Model

• Dual Behaviour of Matter (de Broglie Hypothesis):
  • Just like radiation, matter also exhibits dual behaviour (wave and particle).
  • de Broglie Wavelength (λ): λ = h/mv = h/p
    (m = mass, v = velocity, p = momentum).
  • Significant only for microscopic particles (like electrons) due to their small mass.
• Heisenberg's Uncertainty Principle:
  • It is impossible to determine simultaneously and precisely both the position and the momentum (or velocity) of a microscopic particle.
  • Mathematically: Δx ⋅ Δp ≥ h/4π or Δx ⋅ mΔv ≥ h/4π
    (Δx = uncertainty in position, Δp = uncertainty in momentum, Δv = uncertainty in velocity).
  • Rules out the existence of definite paths or trajectories (orbits) as proposed by Bohr. Introduces the concept of probability.

6. Quantum Mechanical Model of Atom

• Based on dual nature and uncertainty principle. Describes electron behaviour using wave functions.
• Schrödinger Wave Equation: (Not required to solve, just understand its significance) A differential equation whose solutions (wave functions, ψ) describe the energy and probability of finding an electron in a region of space.
• Orbitals: The region in space around the nucleus where the probability of finding an electron (ψ²) is maximum (typically >90%). Orbitals replace the concept of orbits.
• Quantum Numbers: Address/description of an electron in an atom. Derived from the solution of the Schrödinger equation.
  • Principal Quantum Number (n):
    • Determines the main energy shell and average distance from the nucleus (size).
    • Values: n = 1, 2, 3, ... (K, L, M, ... shells).
    • Maximum number of electrons in a shell = 2n².
  • Azimuthal/Angular Momentum Quantum Number (l):
    • Determines the subshell within a shell and the shape of the orbital.
    • Values: l = 0, 1, 2, ..., (n-1).
    • l=0 (s subshell, spherical), l=1 (p subshell, dumbbell), l=2 (d subshell, complex), l=3 (f subshell, more complex).
    • Number of orbitals in a subshell = 2l + 1.
    • Orbital angular momentum = √[l(l+1)] h/2π.
  • Magnetic Quantum Number (m_l):
    • Determines the orientation of the orbital in space relative to a magnetic field.
    • Values: m_l = -l, ..., 0, ..., +l (total 2l+1 values).
    • For l=0 (s), m_l=0 (1 orientation).
    • For l=1 (p), m_l=-1, 0, +1 (3 orientations: p_x, p_y, p_z).
    • For l=2 (d), m_l=-2, -1, 0, +1, +2 (5 orientations: d_xy, d_yz, d_xz, d_x²-y², d_z²).
  • Electron Spin Quantum Number (m_s):
    • Describes the intrinsic angular momentum (spin) of the electron. Represents the two possible spin orientations (clockwise or anti-clockwise).
    • Values: +1/2 (spin up, ↑) or -1/2 (spin down, ↓).
    • An orbital can hold a maximum of two electrons, and they must have opposite spins (Pauli Exclusion Principle).
• Shapes of Atomic Orbitals:
  • s-orbitals: Spherical, non-directional. Probability of finding electron depends only on distance from nucleus. Have (n-1) radial nodes.
  • p-orbitals: Dumbbell shaped, directional along axes (p_x, p_y, p_z). Have one nodal plane passing through the nucleus. Degenerate (same energy) in absence of external fields.
  • d-orbitals: Mostly double dumbbell shape (d_xy, d_yz, d_xz, d_x²-y²) or dumbbell with a collar/donut (d_z²). Have two nodal planes/surfaces. Degenerate.
  • Nodes: Regions where the probability of finding the electron (ψ²) is zero.
    • Radial nodes = n - l - 1
    • Angular nodes = l
    • Total nodes = n - 1
• Energies of Orbitals:
  • Hydrogen Atom: Energy depends only on 'n'. Orbitals within the same shell are degenerate (e.g., 2s = 2p, 3s = 3p = 3d).
  • Multi-electron Atoms: Energy depends on both 'n' and 'l' due to electron-electron repulsions and shielding effect.
    • Shielding/Screening Effect: Repulsion of outer electrons by inner electrons, reducing the effective nuclear charge (Z_eff) experienced by outer electrons.
    • Penetration Effect: Orbitals with lower 'l' values (s > p > d > f for the same 'n') penetrate closer to the nucleus and experience higher Z_eff, hence are lower in energy.
    • Order of Energy: Generally follows the (n+l) rule:
      1. Orbitals fill in increasing order of (n+l).
      2. If (n+l) is the same, the orbital with lower 'n' fills first.
      • Order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p ...

7. Filling of Orbitals & Electronic Configuration

• Aufbau Principle: Electrons first occupy the lowest energy orbital available.
• Pauli Exclusion Principle: No two electrons in an atom can have the same set of all four quantum numbers. (Hence, max 2 electrons per orbital with opposite spins).
• Hund's Rule of Maximum Multiplicity: Pairing of electrons in the orbitals belonging to the same subshell (degenerate orbitals) does not occur until each orbital is singly occupied with parallel spin.
• Electronic Configuration: Distribution of electrons into various orbitals. Represented as n lˣ (e.g., 1s², 2s², 2p⁶). Can also use orbital diagrams (boxes with arrows).
• Stability of Half-filled and Fully-filled Subshells: Configurations with exactly half-filled (p³, d⁵, f⁷) or completely filled (p⁶, d¹⁰, f¹⁴) subshells are exceptionally stable due to:
  • Symmetry: Symmetrical distribution of electrons leads to stability.
  • Exchange Energy: Electrons with the same spin in degenerate orbitals can exchange their positions, releasing energy (exchange energy). More exchanges possible for half/fully filled cases, leading to greater stability.
• Exceptions: Chromium (Cr, Z=24) is [Ar] 3d⁵ 4s¹ (not [Ar] 3d⁴ 4s²). Copper (Cu, Z=29) is [Ar] 3d¹⁰ 4s¹ (not [Ar] 3d⁹ 4s²).

Multiple Choice Questions (MCQs)

1. Which experiment led to the conclusion that most of the space in an atom is empty?
   a) Millikan's oil drop experiment
   b) Cathode ray discharge tube experiment
   c) Alpha-particle scattering experiment
   d) Photoelectric effect experiment

2. The number of angular nodes and radial nodes in a 4d orbital are, respectively:
   a) 2, 1
   b) 1, 2
   c) 2, 2
   d) 3, 0

3. Which of the following sets of quantum numbers is NOT permissible for an electron in an atom?
   a) n=3, l=2, m_l=-1, m_s=+1/2
   b) n=4, l=0, m_l=0, m_s=-1/2
   c) n=2, l=2, m_l=-1, m_s=+1/2
   d) n=1, l=0, m_l=0, m_s=+1/2

4. The energy of a photon is 3.0 × 10⁻¹⁹ J. What is its wavelength? (h = 6.6 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s)
   a) 660 nm
   b) 66 nm
   c) 6.6 nm
   d) 6600 nm

5. Which principle/rule states that pairing of electrons in degenerate orbitals occurs only after each orbital is singly occupied?
   a) Aufbau Principle
   b) Pauli Exclusion Principle
   c) Hund's Rule
   d) Heisenberg's Uncertainty Principle

6. What is the correct electronic configuration of Copper (Cu, Z=29)?
   a) [Ar] 4s² 3d⁹
   b) [Ar] 4s¹ 3d¹⁰
   c) [Ar] 4s¹ 3d⁹ 4p¹
   d) [Ar] 3d¹⁰ 4p¹

7. The Bohr radius for the first orbit of a hydrogen atom is 0.529 Å. What is the radius of the second orbit of He⁺ ion?
   a) 0.529 Å
   b) 1.058 Å
   c) 0.2645 Å
   d) 2.116 Å

8. Which of the following species are isoelectronic?
   (i) O²⁻ (ii) F⁻ (iii) Na⁺ (iv) Mg²⁺ (v) Al²⁺
   a) (i), (ii), (iii) only
   b) (i), (ii), (iii), (iv) only
   c) (i), (ii), (iii), (v) only
   d) All five

9. The uncertainty in the position of an electron (mass = 9.1 × 10⁻³¹ kg) moving with a velocity of 3 × 10⁴ m/s accurate up to 0.011% will be: (h = 6.6 × 10⁻³⁴ J s)
   a) 1.75 × 10⁻² m
   b) 3.50 × 10⁻² m
   c) 1.75 × 10⁻³ m
   d) 3.50 × 10⁻³ m

10. The transition of an electron in a hydrogen atom from n=4 to n=2 corresponds to which spectral series?
    a) Lyman series
    b) Balmer series
    c) Paschen series
    d) Brackett series

Answer Key for MCQs:

1. c
2. a (For 4d: n=4, l=2. Angular nodes = l = 2. Radial nodes = n - l - 1 = 4 - 2 - 1 = 1)
3. c (For n=2, possible l values are 0 and 1 only. l=2 is not allowed)
4. a (E = hc/λ => λ = hc/E = (6.6 × 10⁻³⁴ × 3 × 10⁸) / (3.0 × 10⁻¹⁹) = 6.6 × 10⁻⁷ m = 660 nm)
5. c
6. b
7. b (r_n = 0.529 × n²/Z Å. For He⁺, Z=2. For n=2, r₂ = 0.529 × 2²/2 = 0.529 × 2 = 1.058 Å)
8. b (O²⁻, F⁻, Na⁺, Mg²⁺ all have 10 electrons. Al²⁺ has 11 electrons)
9. c (Δv = 0.011% of 3 × 10⁴ m/s = (0.011/100) × 3 × 10⁴ = 3.3 m/s. Δx ⋅ mΔv ≥ h/4π => Δx ≥ h / (4πmΔv) ≈ (6.6 × 10⁻³⁴) / (4 × 3.14 × 9.1 × 10⁻³¹ × 3.3) ≈ 1.75 × 10⁻³ m)
10. b (For Balmer series, n₁=2)

Make sure you understand the concepts behind each point and MCQ. Revise the formulas and definitions regularly. Good luck with your preparation!