A Level Physics Notes: Nuclear Physics - The Bohr Model of the Atom
The most important properties of atomic and molecular structure may be illustrated using a simplified picture of an atom, similar to the solar system, called the Bohr Model.
A Planetary Model For The Atom
In the Bohr Model the neutrons and protons (symbolized by red and blue balls in the adjacent image) occupy a dense central region called the nucleus, and the electrons orbit the nucleus much like planets orbiting the Sun.
This similarity between a planetary model and the Bohr Model of the atom ultimately arises because the attractive gravitational force in a solar system and the attractive Coulomb (electrical) force between the positively charged nucleus and the negatively charged electrons in an atom are mathematically of the same form - both gravitational and electric forces obey inverse square laws - but the intrinsic strength of the Coulomb interaction is much larger than that of the gravitational interaction; in addition, there are positive and negative electrical charges so the Coulomb interaction can be either attractive or repulsive, but gravitation is always attractive.
Angular Momentum and Energy are Quantized
The basic feature of quantum mechanics that is incorporated in the
Bohr Model and that is completely different from the analogous
planetary model is that the angular momentum is quantized – it can
only come in multiples of a quantity
called
Planck's constant,
This
means that only certain orbits are allowed, illustrated above. This
leads also to the quantization of energy.
The adjacent figure shows such quantized energy levels for the
hydrogen atom. These levels are labelled by an integer n that is
called a quantum number. The lowest energy state is generally termed
the ground state. The ground state of hydrogen has energy of -13.6eV.
The states with successively more energy than the ground state are
called the first excited state, the second excited state, and so on.
Beyond an energy called the ionization potential the single electron
of the hydrogen atom is no longer bound to the atom. Then the energy
levels form a continuum. The energy of each excited state is given by
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Atomic Excitation and De - excitation
Atoms can make transitions between the orbits allowed by quantum mechanics by absorbing or emitting exactly the energy difference between the orbits. The following figure shows an atomic excitation cause by absorption of a photon and an atomic de-excitation caused by emission of a photon.
In each case the wavelength of the emitted or absorbed light is exactly such that the photon carries the energy difference between the two orbits. This energy us given by the formula