Rutherford Alpha Scattering and Atomic Structure

Rutherford Alpha Scattering Experiment

Rutherford — A beam of alpha particles (positively charged helium nuclei) was directed at a very thin gold foil to analyze the scattering behavior and deduce atomic structure.

1. Most particles passed through the foil with little or no deflection.
2. Some alpha particles were slightly deflected and passed through with difficulty.
3. A few particles bounced back from the gold foil.

Conclusion: The atom is mostly empty space with a small, dense, positively charged nucleus at its center and electrons distributed around it. Electrons were initially considered to move in orbits around the nucleus.

Limitations: If electrons moved in circular orbits they would undergo centripetal acceleration and, according to classical electrodynamics, radiate energy. This radiation would cause them to lose energy and spiral into the nucleus, which does not occur in stable atoms.

Atomic Emission and Absorption Spectra

Emission spectrum: When a gaseous substance is heated or subjected to an electric discharge, it emits light. The emitted radiation consists of specific wavelengths (lines) characteristic of the element; this pattern is the emission spectrum.

Absorption spectrum: When a continuous light beam passes through a gas sample and then through a dispersive element (prism or diffraction grating), certain wavelengths are absorbed by the gas. The resulting pattern of missing wavelengths is the absorption spectrum.

Bohr Model and Postulates

Bohr — Based on Planck's ideas, Niels Bohr proposed the following:

1. Electrons (e^-) revolve around the nucleus in certain stable circular orbits without emitting energy.
2. Each orbit corresponds to a quantized energy level that increases with distance from the nucleus. Energy is emitted or absorbed only when an electron transitions between these levels.
3. Only those orbits are allowed for which the electron's angular momentum is an integer multiple of h/2π: L = n·(h/2π), where n is an integer.

Pauli Exclusion Principle

Pauli exclusion principle: An electron in an atom is described by four quantum numbers. No two electrons in the same atom can have the same set of all four quantum numbers.

Quantum-Mechanical Model

The quantum-mechanical model is the current model of the atom, developed in the 1920s by Heisenberg and Schrödinger.

• Wave–particle duality: De Broglie proposed that material particles have wave properties; any moving particle has an associated wavelength.
• Uncertainty principle: Heisenberg stated that it is impossible to determine simultaneously the exact position and momentum of an electron.

The equations of the quantum-mechanical model describe the behavior of electrons in atoms, capturing their wave character and the inability to predict exact trajectories. This established the concept of an orbital: a region of space where the probability of finding an electron is high.

Quantum Numbers

Electrons in atoms are described by four quantum numbers that determine their energy, shape, orientation, and spin.

Principal Quantum Number (n)

Principal (n): The electron energy level and orbital size. n takes integer values 1, 2, 3, ... (commonly 1 to 7 for chemistry).

Azimuthal (Secondary) Quantum Number (l)

Secondary / azimuthal (l): The energy sublevel and orbital shape. l takes integer values from 0 to n − 1.

Magnetic Quantum Number (m_l)

Magnetic (m): The orientation of the orbital in space. m_l ranges from −l to +l.

Spin Quantum Number (m_s)

Spin (s): The intrinsic spin of the electron. m_s can be +1/2 or −1/2.