Bohrs Model of the Nuclear Atom

The structure of the atom is completely nanophysical, requiring quantum mechanics for its description. Bohr's semi-classical model of the atom was a giant step toward this understanding, and still provides much useful information. By introducing, in 1913, a completely arbitrary "quantum number", Bohr [1] was able to break the long-standing failure to understand how an atom could have sharply defined energy levels. These levels were suggested by the optical spectra, which were composed of sharp lines.

Bohr's model is planetary in nature, with the electron circling the nucleus. The model was based on information obtained earlier: that the nucleus of the atom was a tiny object, much smaller in size than the atom itself, containing positive charge Ze, with Z the atomic number, and e the electron charge, 1.6 x 10~19C. The nucleus is much more massive than the electron, so that its motion will be neglected.

Bohr's model describes a single electron orbiting a massive nucleus of charge +Ze. The attractive Coulomb force F = kZe2/r2, where k = (4jt£0)_1 = 9 x 109 Nm2/C2, balances mev2/r, which is the mass of the electron, me = 9.1 x 10_31lcg, times the required acceleration to the center, v2/r. The total energy of the motion, E = mv2/2-kZe2/r, adds up to -kZe2/2r. This is true because the kinetic energy is always -0.5 times the (negative) potential energy in a circular orbit, as can be deduced from the mentioned force balance.

There is thus a crucial relation between the total energy of the electron in the orbit, E, and the radius of the orbit, r.

This classical relation predicts collapse (of atoms, of all matter): for small r the energy is increasingly favorable (negative). So the classical electron will spiral in toward r = 0, giving off energy in the form of electromagnetic radiation. All chemical matter is unstable to collapse in this firm prediction of classical physics.

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