The Bohr model of the atom is successful in describing the spectra of atomic hydrogen and hydrogen-like ions. One of the basic assumptions of the model is that the electron can only exist in certain orbits such that its angular momentum, mvr, is an integral multiple of , where h is Planck’s constant. Assuming circular orbits and a Coulomb force of attraction between electron and proton, the energies of the quantum states for hydrogen are

where k is the Coulomb constant, e is the charge on the electron, and n is an integer called a quantum number.

If the electron in the hydrogen atom jumps from an orbit whose quantum number is n_i to an orbit whose quantum number is n_f , it emits a photon of frequency f, given by

Bohr’s correspondence principal states that quantum mechanics is in agreement with classical physics when the quantum numbers for a system are very large.

One of the many great successes of quantum mechanics is that quantum numbers n, , and associated with atomic structure arise directly from the mathematics of the theory. The quantum number n is called the principal quantum number, is the orbital quantum number, and is the orbital magnetic quantum number. In addition, a fourth quantum number, called the spin magnetic quantum number, m_s , is needed to explain certain features of atomic structure.

An understanding of the periodic table of elements became possible when Pauli formulated the exclusion principal, which states that no two electrons in an atom can never be in the same quantum state, that is, no two electrons in the same atom can have the same set of quantum numbers, n, , , and m_s.

Characteristic x-rays are produced when a bombarding electron collides with an electron in an inner shell of an atom with sufficient energy to remove the electron from the atom. The vacancy thus created is filled when an electron in a higher level drops down into the level containing the vacancy.

© Nathan Alpert 2001