Rutherford's model Knowledge-Based Study

Study notes

1. Background and Setup

   Prior to 1911, J.J. Thomson's plum pudding model described the atom as a uniform sphere of positive charge containing embedded electrons. To test this distribution of charge and mass, Ernest Rutherford, along with Hans Geiger and Ernest Marsden, directed a beam of high-energy, positively charged alpha ($\alpha$) particles emitted from a radioactive source toward an extremely thin sheet of gold foil.

   Surrounding the gold foil was a circular fluorescent zinc sulfide ($\text{ZnS}$) screen that emitted tiny flashes of light (scintillations) whenever an alpha particle struck it, allowing the deflection angles of the particles to be measured accurately.

   Key Observations and Inferences

   The results of the scattering experiment were unexpected based on the plum pudding model:

   • Observation: Most alpha particles passed directly through the gold foil without any detectable deflection.
     Inference: The major portion of the atom consists of empty space.
   • Observation: A small fraction of alpha particles suffered deflections through small angles.
     Inference: There is a concentration of positive charge within the atom that exerts a repulsive electrostatic force on the positively charged alpha particles.
   • Observation: Very few alpha particles (approximately 1 in 20,000) were deflected by large angles, exceeding 90°, with some rebounding directly back.
     Inference: The entire positive charge and nearly all the mass of the atom are concentrated in an extraordinarily small volume at the center of the atom, termed the nucleus.

   Postulates of the Nuclear Model

   Based on the experimental data, Rutherford proposed the nuclear model of the atom, often called the planetary model:

   1. The Nucleus: The positive charge and almost the entire mass of an atom are densely concentrated in a central region called the nucleus. The radius of the nucleus is on the order of $10^{-15}\text{ m}$, which is negligible compared to the atomic radius of about $10^{-10}\text{ m}$.
   2. Extranuclear Electrons: Electrons revolve around the nucleus at high speeds along circular paths, analogous to planets orbiting the Sun.
   3. Electrostatic Balance: Electrostatic forces of attraction between the positively charged nucleus and negatively charged electrons hold the atom together, maintaining overall electrical neutrality.

   Limitations and Unresolved Questions

   Despite successfully disproving the plum pudding model, Rutherford's nuclear model faced significant theoretical limitations:

   • Instability of the Atom: According to classical electromagnetic theory (Maxwell's equations), an accelerating charged particle continuously emits electromagnetic radiation and loses energy. Since electrons moving in circular orbits undergo continuous centripetal acceleration, they should steadily lose kinetic energy and spiral inward, collapsing into the nucleus within $10^{-8}\text{ s}$. In reality, atoms are stable.
   • Atomic Line Spectra: If electrons spiraled inward continuously emitting radiation of all wavelengths, atoms would produce continuous spectra. Instead, experimental observations show that atoms produce discrete line emission spectra.
   • Electronic Structure: The model did not provide any explanation for the precise arrangement or specific energy levels of electrons around the nucleus.