Biomedical Engineering Reference
In-Depth Information
for
that shell, which is highest for the electrons at the innermost shell. The energy required to
move an electron from an inner shell to an outer shell is equal to the difference in binding
energies between the two shells. This energy requirement represents one of the natural
characteristics of an element. The elementary particle of electromagnetic radiation is the
photon
The amount of energy required to eject an electron from an orbit is the
binding energy
. When the binding energy is released as a photon, in the case of transition of an
electron from an outer shell to an inner shell, it is known as a characteristic x-ray. However,
if instead of the emission of a photon the energy is transferred to another orbital electron,
called an Auger electron, it will be ejected from orbit. The probability for the yield of a
characteristic x-ray in such a transition is known as fluorescent yield.
Protons and neutrons (also known as nucleons) experience a short-range nuclear force
that is far greater than the electromagnetic force of repulsion between the protons. The
movement of nucleons is often described by a shell model, analogous to orbital electrons.
However, only a limited number of motions are allowed, and they are defined by a set of
nuclear quantum numbers. The most stable arrangement is known as the ground state.
The other two broad arrangements are (1) the metastable state, when the nucleus is unstable
but has a relatively long lifetime before transforming into another state; and (2) the excited
state, when the nucleus is so unstable that it has only a transient existence before transform-
ing into another state. Thus, an atomic nucleus may have separate existence at two energy
levels, known as
(both have the same Z as well as the same A). An unstable nucleus
ultimately transforms itself to a more stable condition, either by absorbing or releasing
energy (photons or particles) to a nucleus at ground state. This process is known as radio-
active transformation or decay. As just stated, naturally occurring heavier elements, having
Z greater than 83, are all unstable.
Assessment of nuclear binding energy is important in determining the relative stability
of a nuclide. This binding energy represents the minimum amount of energy necessary to
overcome the nuclear force required to separate the individual nucleons. This can be
assessed on the basis of mass-energy equivalence as represented by
isomers
2
, where
E
¼
mc
E, m
,
and
represent energy, mass, and speed of light, respectively. This has led to the common
practice of referring to masses in terms of electron-volts (eV). The mass of an atom is always
found to be less than the sum of the masses of the individual components (neutrons, pro-
tons, and electrons). This apparent loss of mass (
c
), often called mass defect or deficiency,
is responsible for the binding energy of the nucleus and is equivalent to some change in
energy (
D
m
2
). As mentioned previously, the mass of a neutral carbon-12 atom has been
accepted as 12.0 atomic mass units (amu). The sum of the masses of the components
of
D
mc
12
however, is 12.10223 amu. The difference in masses (0.10223 amu) is equivalent to
95.23 mega-electron-volts (MeV) of binding energy for this nucleus, or 7.936 MeV/nucleon
(obtained by dividing MeV by A
C,
12) for carbon-12. For nuclei with atomic mass numbers
greater than 11, the binding energy per nucleon ranges between 7.4 and 8.8 MeV. One
atomic mass unit (1 amu), therefore, is equal to 1.6605655
¼
10
24
g or, using the mass-
energy relation, is equivalent to 931.502 MeV. The world record for proton acceleration,
set in November 2009 by the Large Hadron Collider in Geneva, stands at an energy level
of 1.18 trillion eV. The resting mass of an electron, on the other hand, is very small: only
0.511 MeV.
