The Hydrogen atom

Hydrogen is the simplest atom (one proton and one electron), but it provides a rich topic for study. The wave-function aspect of quantum mechanics prevents the electron from collapsing into an infinitesimally small orbit with an infinite negative energy. In classical physics, an attractive ~1/r potential could have arbitrarily small orbitals with arbitrarily large binding energies. In quantum physics, the lowest energy orbital is called the ground state. Solving the Schroedinger equation for an electron in the Coulomb potential provides the ground state properties of the hydrogen atom.

Ground state properties of hydrogen

  Average orbital radius Binding energy
ground state of hydrogen atom
ground state of higher charge atom
excited state of higher charge atom  

The subscript 0 which refers to the ground state corresponds to n = 1, for historical reasons. The radius of the ground state of hydrogen is called the Bohr radius; it is named for Niels Bohr, who derived it by a famous but incorrect argument.

When electrons make a jump from one energy level (a specific value of n) to another energy level, a photon is emitted that carries away the necessary energy to satisfy energy conservation. The inverse wavelength (which is proportional to the energy) of the light is then propotional to the change in energy:

R is known as Rydberg's constant. The beginning level is denoted by m and the final level is denoted by n. For n = 1, the various wavelengths (m = 2,3,4...) are known as the Lyman series. The Balmer series is the series where n = 2 and the Paschen series is for n = 3. The values of the wavelengths are often called spectral lines because of the lines that appear in diffraction experiments. For a hot hydrogen source, where the atoms are excited thermally and then deexcite via the emission of photons, the Balmer series is in the visible range.

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