Unit 3: Atomic Structure

Unit 3: Atomic Structure (8 Teaching Hours)

1. Rutherford’s Atomic Model

• Rutherford's model (1911) was based on his famous gold foil experiment.
• Key points:
  • The atom consists of a small, dense, positively charged nucleus at the center.
  • Electrons revolve around the nucleus in circular orbits.
  • Most of the atom's volume is empty space.

2. Limitations of Rutherford’s Atomic Model

• Stability of the atom: According to classical physics, revolving electrons should emit radiation, lose energy, and spiral into the nucleus, leading to the collapse of the atom, which doesn’t happen.
• Atomic spectra: Rutherford's model couldn’t explain the discrete line spectra of atoms (especially hydrogen).

3. Bohr’s Atomic Model and its Postulates

Bohr’s model (1913) modified Rutherford’s idea by incorporating quantum concepts.

• Key Postulates:
  1. Quantized orbits: Electrons move in specific, quantized orbits without radiating energy.
  2. Energy levels: Each orbit corresponds to a fixed energy level, and an electron can only lose or gain energy by jumping between levels.
  3. Energy absorption and emission: When electrons move to higher energy levels, they absorb energy; when they fall back to lower levels, they emit energy in the form of light.
• Application: This model successfully explained the hydrogen atom's spectrum and energy levels.

4. Spectrum of Hydrogen Atom

• The hydrogen atom emits light in distinct spectral lines, known as the line spectrum.
• Bohr’s model explained these lines as electron transitions between quantized energy levels:
  • Lyman series (UV): Electrons falling to the n = 1 level.
  • Balmer series (Visible): Electrons falling to the n = 2 level.
  • Paschen series (IR): Electrons falling to the n = 3 level, and so on.

5. Defects of Bohr’s Theory

• Limited to hydrogen-like atoms: Bohr’s model only works for single-electron systems like hydrogen and can’t explain multi-electron atoms.
• No explanation for fine spectral lines: The model doesn’t account for the splitting of spectral lines due to electron spin or magnetic fields.
• Wave-particle duality: Bohr's model doesn't incorporate the wave-like behavior of electrons.

6. Quantum Mechanical Model: de Broglie’s Wave Equation

• de Broglie’s Hypothesis: Particles, like electrons, exhibit both particle and wave-like properties.
  • Wave Equation: $\lambda = \frac{h}{mv}$
    Where $\lambda$ is the wavelength, $h$ is Planck's constant, $m$ is mass, and $v$ is velocity.
  • This explains why electrons exist in quantized orbits, as only certain wavelengths can fit into the electron's orbit.

7. Heisenberg’s Uncertainty Principle

• Uncertainty Principle: It is impossible to know both the exact position and momentum of an electron simultaneously with absolute precision.
  • Mathematically: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$
  • This challenges the notion of defined orbits from Bohr's model.

8. Concept of Probability

• Instead of precise orbits, quantum mechanics describes the position of electrons in terms of probability distributions.
• Electrons are most likely found in regions called orbitals, where the probability of finding an electron is highest.

9. Quantum Numbers

• Principal Quantum Number (n): Defines the size and energy of an orbital.
• Azimuthal Quantum Number (l): Defines the shape of the orbital (s, p, d, f).
• Magnetic Quantum Number (mₗ): Defines the orientation of the orbital in space.
• Spin Quantum Number (mₛ): Describes the spin direction of the electron (+½ or -½).

10. Orbitals and Shape of s and p Orbitals

• s orbitals: Spherical in shape, with increasing size as n increases.
• p orbitals: Dumbbell-shaped, oriented along the x, y, and z axes (px, py, pz).

11. Aufbau Principle

• Electrons fill the lowest energy orbitals first before moving to higher energy orbitals.
• Electron configuration follows the sequence of energy levels:
  1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on.

12. Pauli’s Exclusion Principle

• No two electrons in the same atom can have the same set of four quantum numbers.
• This means each orbital can hold a maximum of two electrons, with opposite spins.

13. Hund’s Rule

• Electrons fill degenerate orbitals (orbitals of the same energy, like p orbitals) singly before pairing up, to minimize electron repulsion.

14. Electronic Configurations of Atoms and Ions (up to Atomic Number 30)

• Example:
  • Hydrogen (Z = 1): 1s¹
  • Carbon (Z = 6): 1s² 2s² 2p²
  • Phosphorus (Z = 15): 1s² 2s² 2p⁶ 3s² 3p³
  • Calcium (Z = 20): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²
  • Zinc (Z = 30): 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s²