Comprehensive Study Notes on Atomic Models: Rutherford and Bohr

Rutherford’s Gold Foil Experiment (1909)

• Context and Motivation: In 1909, Ernest Rutherford undertook a series of experiments to investigate the structure of the atom, testing the prevailing Thomson (Plum Pudding) model.
• The Thomson Model Prediction: According to the Thomson model, which proposed a diffuse positive charge with embedded electrons, alpha ($\alpha$) particles fired at an atom would only be slightly deflected as they passed through.
• Experimental Procedure:
  • An alpha ($\alpha$) emitter was contained within a protective lead box to focus the radiation into a concentrated beam.
  • Rutherford fired these alpha particles at an extremely thin sample of gold foil.
  • A Zinc Sulfide (Zn-Su) detector was placed around the gold foil to observe and record the paths and impact points of the particles.
• Discovery: Contrary to expectations, Rutherford observed that while many particles passed through, some were deflected through very large angles, and some were even reflected straight back toward the source.

Observations and Conclusions of the Alpha Scattering Experiment

• Observation 1: The majority of alpha particles (almost all) passed straight through the gold foil and were not deflected.
  • Conclusion: The atom is mostly empty space.
• Observation 2: A few alpha particles (not many) bounced directly back toward the radiation source.
  • Conclusion: The atom must contain a dense core, referred to as the nucleus, which is very small relative to the total size of the atom and contains most of its mass.
• Observation 3: several alpha particles (some) passed through the gold foil but were deflected at various angles.
  • Conclusion: The nucleus must be positively charged. This conclusion is based on the law of repulsion, as the positively charged alpha particles were pushed away by the central positive charge of the nucleus.

Bohr’s Atomic Model and Circular Orbits

• General Structure: Niels Bohr proposed an atomic model where electrons orbit a central, positively charged nucleus.
• Subatomic Particles: The nucleus is composed of protons (positive) and neutrons (neutral), while electrons (negative) reside in orbits.
• Nature of Orbits:
  • Orbits are circular and stable.
  • Orbits exist at discrete, quantized energy levels, meaning electrons cannot exist between these specific paths.

Bohr’s Three Postulates

• Postulate 1: Stationary States: Electrons exist in stationary states, which are defined as orbits of certain radii with quantized energies.
  • Energy Level Formula: The energy of a specific state can be represented by: $E = \frac{E_1}{n^2}$
• Postulate 2: Transitions and Electromagnetic radiation (EMR): Electrons have the capacity to move between stationary states by either absorbing or emitting electromagnetic radiation.
  • Photon Energy: The energy of the absorbed or emitted photon is equivalent to the difference in energy between the two states involved in the transition.
  • Formula: $E = E_f - E_i$
• Postulate 3: Quantization of Angular Momentum: The angular momentum of an electron within an orbit is quantized, meaning it can only take on specific integer multiples of a base value.
  • Formula: $\text{Angular momentum} = n \frac{h}{2\pi}$

Evidence Supporting Bohr's Atomic Model

• Hydrogen Emission Spectrum: Bohr’s model was primarily based on and supported by observations of the hydrogen emission spectrum.
• Mechanism of Emission: Emission lines are produced when electrons transition from higher energy states (excited states) to lower energy states, releasing energy in the form of light.
• Transition Energy Formula: The energy change ($\Delta E$) associated with these transitions is given by: $\Delta E = h\nu = 13.6 \times \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$
• Spectral Series and Wavelengths: Transitions between different energy levels ($n$ states) result in specific series of spectral lines categorized by their wavelength and region of the electromagnetic spectrum:
  • Lyman Series: Transitions ending at the $n = 1$ state; these falls within the Ultraviolet range.
  • Balmer Series: Transitions ending at the $n = 2$ state; these are visible to the human eye. Key observed wavelengths include:
    • $410.2\,nm$ (Violet)
    • $434.1\,nm$ (Violet)
    • $486.1\,nm$ (Blue-green)
    • $656.3\,nm$ (Red)
  • Paschen Series: Transitions ending at the $n = 3$ state; these falls within the Infrared range.