RADIATION PROTECTION - ILEA

2 | Energy Relationships in the Hydrogen Atom 11
companying effects, but to start, let us review the range of energies that
one can encounter in radiation protection.
2 Energy Relationships in the Hydrogen Atom
How does one begin to comprehend this enormous energy range from the
viewpoint of radiation protection? The energy relations in the hydrogen
atom make a good reference point for comparisons with both higher energies
and lower energies.
An isolated hydrogen atom consists of a heavy, positively charged particle
at the center, the proton, around which revolves a light, negatively
charged particle, the electron, held in orbit by the electromagnetic force.
The electron is restricted to specific orbits, as given by the principles of
quantum mechanics, and each orbit is associated with a specific energy
level. When the electron is in its lowest energy level, that is, at the closest
distance it is allowed (by the uncertainty principle) to come to the proton,
the atom is said to be in its ground state.
It takes energy to move the electron to orbits at greater distances from
the proton; when the electron occupies an outer orbit, the atom is said to
be in an excited state. Atoms revert from an excited state to the ground state
with the emission of radiation as packets of electromagnetic energy called
photons, which carry energies equal to the difference in energy levels between
the two states.
The greatest energy change occurs when the electron is moved so far
from the proton that the electromagnetic force between them is negligible.
At this point, the atom is said to be ionized. It takes 13.6 electron volts to
transfer an electron from the ground state of the hydrogen atom to the
ionized state. Radiations with particle energies greater than the energy
needed to remove an outermost electron from an atom are called ionizing
radiations.
For the lower-energy states, the differences in energy levels in hydrogen
(and also the energies of the photons emitted) is given by a very simple
formula:
E =−13.6(1/n 1 2 − 1/n 2 2 ) eV (1.1)
n 1 and n 2 are integers corresponding to an electron’s orbit (orbit 1 is nearest
the proton, orbit 2 is the next orbit out, orbit 3 is further out still, and
so on).
Since it is only the difference in energy levels that is relevant, the formula
can be rewritten to express energy levels in the hydrogen atom. These are
not the actual values of the energy levels, but their differences give the en-