Unit 3: Atomic Structure

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.

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).

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.

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.

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.

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.

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.

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.

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).

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).

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.

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.

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

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