Energy States and Photons

One of the great breakthroughs of early 20th-century physics, embodied in the Bohr model of atomic structure, was the recognition that atoms can exist only in certain states or configurations, each with its own specific energy. In the simple Bohr picture of the hydrogen atom, different states correspond to electron orbits of different radii, each with a well-defined energy equal to the sum of the kinetic and potential energies of the electron in its orbit. This very simple mechanical picture has been subsequently modified by quantum mechanics, but the basic point remains that the possible configurations of an atom correspond to a limited set of states. The discrete energies associated with these states are the allowed energy levels of the atom. The same rule holds for nuclei, although we are not yet able to account theoretically for the exact energy levels of nuclei with as great precision as we can for atoms.

Thus, in broad terms, each atom or nucleus can exist in a state of lowest energy, the so-called ground state, or in one or another state of higher energy, the so-called excited states. With a few exceptions, the excited states are shortlived; that is, they quickly emit their excess energy and the system (atomic or nuclear) reverts to its ground state. The energy lost by the atom in a transition from one excited state to a lower one (or to the ground state) is commonly carried off by electromagnetic radiation.8 For nuclei, a typical time for a transition from an excited state to a lower state is in the neighborhood of 10~12 sec, although very much longer and somewhat shorter lifetimes are also possible.

When an atom (or nucleus) in a state of initial energy Ei makes a transition to a final state of lower energy Ef, the energy carried off in electromagnetic radiation is

Throughout the 19th century, light and (when recognized) other forms of electromagnetic radiation were thought to be properly described by waves. One of the revolutionary new insights of early 20th-century physics was the recognition that light also has particle-like properties. In particular, the electromagnetic radiation corresponding to a single atomic (or nuclear) transition is carried in a single discrete packet, called a photon.

The energy of the photons for a given transition is simply related to the wavelength, or frequency, of the associated radiation:

where X is the wavelength, v is the frequency, and h is a universal constant known as Planck's constant: h = 6.626 x 10~34 joule-sec. Thus, in the transition of Eq. A.8, the photon energy is hv = Ei — Ef. (A.10)

Visible light is associated with transitions involving the outer electrons of atoms or molecules, with photon energies in the neighborhood of several eV (3 eV corresponds to X = 4130 A = 0.413 x 10~6 m). X-rays correspond to transitions involving the inner electrons of atoms, with typical energies of 1 to 100 keV, depending on the atomic number of the atom. Radiative transitions

8 There are two classes of exceptions to this: (a) sometimes the energy can be transferred to an electron in a process known as internal conversion, still leaving the nuclide unchanged; and (b) in some cases an excited state can decay by emitting a particle, such as a beta particle or neutron, thereby changing the atomic number or the mass number of the nuclide.

between nuclear levels typically involve energies in the neighborhood of 100 to 10,000 keV. The photons from nuclei are called gamma rays. There is no difference between these groups of photons other than their energy. In fact, it is possible, although not common, to have gamma rays with energies lower than those of typical x-rays. The names "x-ray" and "gamma ray" date to the times of the original discovery of the then-mysterious radiations. In principle, there is no need for different terms to distinguish between photons from atomic transitions (x-rays) and photons from nuclear transitions (gamma rays), but the terminology is retained, perhaps because it provides a reminder of their physical origin.

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