Atomic models Knowledge-Based Study

Study notes

1. The Indivisible Sphere

   In the early 19th century, John Dalton proposed the first modern scientific atomic theory based on experimental observations of chemical reactions and the laws of definite and multiple proportions.

   Key postulates of Dalton's model include:

   • Matter is composed of extremely small, indivisible particles called atoms.
   • All atoms of a given element are identical in mass and properties, while atoms of different elements differ in mass and chemical behavior.
   • Compounds are formed when atoms of different elements combine in fixed, simple whole-number ratios.
   • Chemical reactions involve the rearrangement of atoms; atoms are neither created nor destroyed during chemical transformations.

   Dalton envisioned the atom as a hard, solid, indivisible sphere, similar to a solid billiard ball. While this model successfully explained conservation of mass and chemical combination, it could not account for electrical phenomena or subatomic structure.

   The Plum Pudding Model

   In 1897, J.J. Thomson performed cathode ray tube experiments and demonstrated that cathode rays are streams of negatively charged particles with a mass far smaller than that of a hydrogen atom. This particle was identified as the electron, proving that atoms are divisible.

   Because ordinary matter is electrically neutral, Thomson concluded that an atom must also contain positive charge to balance the negative electrons. In 1904, he proposed the 'plum pudding' (or raisin cake) model:

   • An atom consists of a uniform sphere of positive charge.
   • Negatively charged electrons are embedded throughout this positive sphere, much like raisins distributed in a pudding.
   • The total negative charge of the embedded electrons equals the total positive charge of the sphere, ensuring overall electrical neutrality.

   Thomson's model was the first to incorporate subatomic particles, but it lacked an explanation for the specific spatial distribution and stability of charges.

   The Gold Foil Experiment

   In 1911, Ernest Rutherford, along with Hans Geiger and Ernest Marsden, directed high-energy, positively charged alpha particles ($\alpha$-particles) at a very thin sheet of gold foil.

   Under Thomson's model, the mass and positive charge were assumed to be spread evenly throughout the atom, so alpha particles were expected to pass through with only negligible deflections. However, the experimental results revealed:

   • Most alpha particles passed straight through the foil without deflection.
   • A small fraction of particles were deflected at moderate angles.
   • A tiny fraction (about 1 in 8,000) bounced back almost directly toward the source.

   Based on these findings, Rutherford deduced:

   • The atom is mostly empty space, which allows most alpha particles to pass through unhindered.
   • All positive charge and virtually all mass of the atom are concentrated in an extremely small, dense central region called the nucleus.
   • Electrons move in the vast space surrounding the nucleus, much like planets orbiting the Sun.

   Rutherford's model could not, however, explain why accelerating charged electrons do not continuously radiate electromagnetic energy and spiral into the nucleus according to classical electrodynamics.

   Quantized Energy Levels

   To resolve the stability problem of Rutherford's atom and to explain the discrete line emission spectra of hydrogen, Niels Bohr introduced a quantum concept in 1913.

   Bohr's key postulates are:

   • Electrons orbit the nucleus only in specific, non-radiating circular paths called stationary orbits or energy levels.
   • Each orbit corresponds to a quantized value of angular momentum given by $L = n\frac{h}{2\pi}$, where $n = 1, 2, 3, \dots$ is the principal quantum number and $h$ is Planck's constant.
   • An electron does not emit radiation while remaining in a permissible orbit.
   • An electron absorbs or emits a photon of electromagnetic radiation only when transitioning between two stationary energy states. The energy of the emitted or absorbed photon is given by $\Delta E = E_{\text{final}} - E_{\text{initial}} = hf$.

   Bohr's model accurately calculated the spectral lines of single-electron systems such as hydrogen, but it failed to predict spectra of multi-electron atoms or explain chemical bonding and fine spectral splitting.

   The Electron Cloud and Orbitals

   In the 1920s, developments in quantum mechanics fundamentally transformed the understanding of atomic structure through Louis de Broglie's hypothesis of matter waves, Werner Heisenberg's uncertainty principle, and Erwin Schrödinger's wave equation.

   Core principles of the modern quantum model include:

   • Wave-Particle Duality: Electrons exhibit both particle-like and wave-like behaviors.
   • Heisenberg Uncertainty Principle: It is impossible to simultaneously determine both the exact position and the exact momentum of an electron: $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$.
   • Atomic Orbitals: Instead of fixed circular paths, an electron is described by a mathematical wave function ($\psi$). The square of the wave function, $|\psi|^2$, represents the probability density of locating an electron in a given region of space around the nucleus.

   Today, the space around the nucleus where the probability of finding an electron is highest (typically defined within a 90% boundary surface) is termed an orbital. Orbitals are characterized by four quantum numbers ($n$, $l$, $m_l$, and $m_s$), providing the foundation for modern chemistry and solid-state physics.