4: The Hydrogen Atom
- Page ID
- 467565
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- 4.1: The Hydrogen Atomic Spectrum
- Gases heated to incandescence were found to emit light with a series of sharp wavelengths. The emitted light analyzed by a spectrometer appears as a multitude of narrow bands of color. These so called line spectra are characteristic of the atomic composition of the gas. One such set of lines in the hydrogen ATOM emission are the Balmer lines, in which a phenomenological relatioshop between frequency and an integer of unknown origin.
- 4.2: The Rydberg Formula and the Hydrogen Atomic Spectrum
- The Rydberg formula is used to describe the wavelengths of spectral lines and was formulated by the Swedish physicist Johannes Rydberg. The Rydberg formula explains the different energies of transition that occur between energy levels. When an electron moves from a higher energy level to a lower one, a photon is emitted. The Hydrogen atom can emit different wavelengths of light depending on the initial and final energy levels of the transition.
- 4.3: Bohr's Hydrogen Atom
- Niels Bohr introduced the atomic Hydrogen model in 1913. He described it as a positively charged nucleus, comprised of protons and neutrons, surrounded by a negatively charged electron cloud. In the model, electrons orbit the nucleus in atomic shells. The atom is held together by electrostatic forces between the positive nucleus and negative surroundings.
- 4.4: The Schrödinger Equation
- The hydrogen atom, consisting of an electron and a proton, is a two-particle system, and the internal motion of two particles around their center of mass is equivalent to the motion of a single particle with a reduced mass.
- 4.5: Other One-Electron Systems
- The quantum mechanical treatment of the hydrogen atom can be extended easily to other one-electron systems such as \(He^+\), \(Li^{2+}\), etc. The Hamiltonian changes in two places. Most importantly, the potential energy term is changed to account for the charge of the nucleus, which is the atomic number of the atom or ion, \(Z\), times the fundamental unit of charge, \(e\).
- 4.6: The Wavefunctions
- The solutions to the hydrogen atom Schrödinger equation are functions that are products of a spherical harmonic function and a radial function.
- 4.7: s-orbitals are Spherically Symmetric
- The hydrogen atom wavefunctions are called atomic orbitals. An atomic orbital is a function that describes one electron in an atom. The radial probability distribution is introduced in this section.
- 4.8: Orbital Angular Momentum and the p-Orbitals
- The physical quantity known as angular momentum plays a dominant role in the understanding of the electronic structure of atoms.