Short Notes: Structure of Atom

2.1 Discovery of Subatomic Particles

The concept of the atom evolved gradually as experiments revealed smaller constituents. Important discoveries are:

• John Dalton (early 1800s): Proposed atom as an indivisible particle and used it to explain chemical reactions.
• J. J. Thomson (1897): Discovered the electron using cathode ray experiments and measured the charge-to-mass ratio of the electron. This showed atoms contain negatively charged particles.
• Robert A. Millikan (1909): Performed the oil-drop experiment and measured the elementary charge (e), allowing calculation of the electron mass from Thomson's ratio.
• Ernest Rutherford (1911): Through alpha-particle scattering (gold foil) experiment, discovered the nucleus-a small, dense, positively charged centre-leading to the nuclear model of the atom.
• James Chadwick (1932): Discovered the neutron, a neutral particle within the nucleus, explaining atomic masses and isotopes.

These experiments established that atoms are composite objects containing electrons, protons and neutrons, and that most of the atom's mass is concentrated in the nucleus.

2.2 Atomic Models

Atomic models were proposed to explain experimental observations. Key models and their main ideas:

• Dalton's model: Atoms are indivisible spheres differing in mass; explained conservation of mass and definite proportions but could not explain electrical phenomena or subatomic structure.
• Thomson's plum-pudding model: Atom as a diffuse positive sphere with embedded electrons; motivated by discovery of the electron but failed to explain scattering results.
• Rutherford's nuclear model: Atom has a tiny, dense, positively charged nucleus containing most mass; electrons move around the nucleus. Explained alpha scattering but could not account for atomic stability or discrete spectral lines.
• Bohr model (1913): Introduced quantised orbits for electrons around the nucleus. Postulates:
  • Electrons move in certain allowed circular orbits without radiating energy.
  • Energy is emitted or absorbed when an electron jumps between orbits; the energy difference corresponds to a photon.
  • Angular momentum of electron in allowed orbit is quantised as mvr = nħ (n = 1, 2, 3...).
  Bohr's model successfully explained the hydrogen emission spectrum and energy levels, with energy for level n given by the familiar expression for hydrogen-like atoms. Its limitations include inability to accurately treat multi-electron atoms and explain fine structure and spectral intensities.

Development of quantum mechanics provided a more general and accurate model.

2.3 Quantum Mechanical Model

The quantum mechanical model describes electrons by wavefunctions rather than fixed orbits. Main points:

• Wavefunction (ψ): Solution of the Schrödinger equation for an electron in an atom. The square of the wavefunction, |ψ|², gives the probability density of finding an electron at a point in space.
• Orbitals: Regions of space with a high probability of containing an electron. Orbitals are labelled as s, p, d, f and have characteristic shapes and energies.
• Heisenberg Uncertainty Principle: It is impossible to simultaneously know the exact position and exact momentum of an electron; therefore electrons are described by probability distributions, not precise paths.
• Advantages over Bohr model: Explains multi-electron atoms, orbital shapes, degeneracy, and spectral details using quantum numbers and electron-electron interactions.

2.4 Quantum Numbers

Quantum numbers arise from solutions of the Schrödinger equation and uniquely describe an electron in an atom. There are four quantum numbers:

• Principal quantum number (n): n = 1, 2, 3, ... . Determines the main energy level and relative size of the orbital. Higher n → higher energy and larger orbital.
• Azimuthal (angular momentum) quantum number (l): l = 0, 1, 2, ..., (n - 1). Determines the shape of the orbital. Common designations: l = 0 (s), 1 (p), 2 (d), 3 (f).
• Magnetic quantum number (m_l): m_l = -l, -l+1, ..., 0, ..., +l. Specifies the orientation of the orbital in space.
• Spin quantum number (m_s): m_s = +1/2 or -1/2. Represents the two possible spin orientations of an electron.

Allowed combinations of these quantum numbers describe each possible electron state (orbital + spin). The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of all four quantum numbers, so each orbital can hold a maximum of two electrons with opposite spins.

2.5 Electronic Configuration Rules

Electronic configuration describes the distribution of electrons among atomic orbitals. The following rules and conventions are used to write correct configurations and to predict the ground-state electron arrangement.

• Aufbau Principle: Electrons occupy orbitals in order of increasing energy, from lowest to highest. A commonly used energy ordering is:
  1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p ...
  This sequence can be memorised using diagonal rules or energy-level diagrams. For multi-electron atoms, orbital energies can shift and produce exceptions.
• Pauli Exclusion Principle: No two electrons in an atom may have identical sets of four quantum numbers. Consequently, an orbital can hold at most two electrons, and they must have opposite spins (↑↓).
• Hund's Rule: For degenerate orbitals (orbitals of the same energy, e.g., the three 2p orbitals), electrons occupy each orbital singly with parallel spins before pairing begins. This minimises electron repulsion and yields the lowest energy arrangement.
• Orbital Capacity: The maximum number of electrons that can occupy orbitals of a given type is:
  • s orbital: 2 electrons
  • p orbitals (three orientations): 6 electrons
  • d orbitals (five orientations): 10 electrons
  • f orbitals (seven orientations): 14 electrons

Additional practical points and examples:

• Writing configurations: List occupied orbitals in increasing energy order with superscripts for electron counts, for example:
  Carbon (Z = 6): 1s² 2s² 2p².
• Noble-gas shorthand: Use the electron configuration of the previous noble gas in brackets to shorten notation. For potassium (Z = 19):
  K: [Ar] 4s¹.
• Orbital diagrams: Represent orbitals as boxes or lines and electrons as arrows (↑ or ↓). Apply Hund's rule when filling degenerate orbitals.
• Exceptions: Some transition elements show deviations from the simple Aufbau order because half-filled and fully-filled subshells have extra stability. Common examples:
  Chromium (Cr, Z = 24): expected 4s² 3d⁴, observed 4s¹ 3d⁵.
  Copper (Cu, Z = 29): expected 4s² 3d⁹, observed 4s¹ 3d¹⁰.
• Ground-state vs excited-state: Ground-state configuration follows the rules above for the lowest energy arrangement. Excited states arise when one or more electrons occupy higher energy orbitals temporarily.
• Example - Oxygen (Z = 8):
  Write configuration: 1s² 2s² 2p⁴.
  Orbital diagram for 2p: three boxes for 2p_x, 2p_y, 2p_z; place four electrons using Hund's rule: ↑ ↑ ↑ ↓ (one orbital has paired electrons).

Summary

The modern picture of the atom is built from experimental discoveries of electrons, protons and neutrons and refined through successive models: Dalton, Thomson, Rutherford, Bohr and finally the quantum mechanical model. Quantum numbers and the rules for electronic configuration (Aufbau principle, Pauli exclusion, Hund's rule) provide a consistent method to describe and predict the arrangement of electrons in atoms, which in turn explains chemical behaviour, periodic trends and spectral properties.