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Nuclear Physics
The Atomic Nucleus
The nucleus of an atom consists of a collection of positively charged protons and neutral neutrons
at the center of the atom. Protons and neutrons are called nucleons. The electrons surrounding
the nucleus take part in chemical reactions, but not nuclear reactions. Protons and neutrons are
made of smaller particles called quarks. The nucleus of an atom occupies 10-12 of the volume of
the atom, yet it contains over 99% of its mass. Atoms are mostly empty space.
Atomic Number and Mass Number
The nucleus of an atom is described using atomic number(Z), mass number(A) and neutron
number(N). The atomic number is equal to the number of protons in the nucleus and determines
the identity of the atom. In a neutral atom, the number of electrons equals the number of protons
and is also equal to Z. If electrons are gained or lost, the resulting particle is an ion of that
element. If protons are gained or lost through nuclear reactions, we say we have formed a
different element. The mass number is the total number of nucleons in the atom, and the neutron
number is the number of neutrons in the atom.
Mass number
atomic number
A
ZX
element symbol
These numbers are related by the equation:
A=Z+N
Nuclear Forces
There are 4 basic forces or types of interaction:
•
gravity
•
electromagnetic
•
strong interaction ("nuclear force")
•
weak interaction (causes some types of radioactive decay)
In the nucleus protons repel each other with the electric Coulomb’s force and would make the
nucleus split unless another force, the "nuclear force" or strong interaction, kept it together.
The nuclear force is attractive at distances about the size of a nucleon and thereafter very quickly
becomes weaker. Thus, for larger nuclei one tends to need more and more nucleons to keep
them stable. At distances shorter than the size of a nucleon it becomes repulsive, preventing the
nucleus from collapsing.
The electromagnetic repulsive force is long range and all the protons in the atom affect each
other. When the nucleus becomes very large (Z > 83), the repulsive force causes part of the
nucleus to be expelled, and we say the nucleus is unstable (undergoes radioactive decay).
Mass Defect
If we add the mass of the nucleons and compare it to the mass of the nucleus, then we will find
that some mass is missing. The difference in mass is called the mass defect (∆m):
∆m = mass of protons + mass of neutrons – mass of nucleus
Einstein discovered that matter could be converted to energy (and vice-versa). The equation that
expresses this mass-energy equivalency is:
E = mc2 (c = 3.00*108 m/s) or ∆E = c2∆m
This missing mass is then a form of energy which may be released if the atom, and especially the
nucleus, changes in such a way that more energy is missing. The missing energy is called
binding energy. The binding energy represents the amount of energy that must be supplied to
break the nucleus into its individual protons and neutrons. Conversely, it is the energy released
when the nucleus is formed from individual protons and neutrons. For a single nucleus, the
magnitude of the binding energy is typically between 10-10 to 10-12 J.
Nuclear Reactions
Transmutation is the process of a nucleus changing into another nucleus. This can happen
spontaneously, as in radioactive decay, or it can happen artificially when scientists add particle(s)
to a nucleus causing it to change. All of the elements with atomic numbers greater than 92 are
created artificially and do not exist in nature. They are called transuranium elements.
In any nuclear reaction the following must always be true:
•
The total atomic number before the reaction must be the same as the total atomic
number after the reaction.
•
The total atomic mass before the reaction must be the same as the total atomic mass
after the reaction.
The first requirement above is the statement of the conservation of charge in nuclear reactions.
The second requirement is the statement of the conservation of nucleon number.
Radioactive Decay
In a nucleus, the repulsion between the positive protons is overcome by the nuclear force or
strong interaction which is attractive at suitable distances. This leads to a certain relation between
the number of protons and neutrons being most stable. The nuclei with less “favourable” ratio of
neutrons to protons are unstable and can split forming nuclei of other elements. This process is
called radioactive decay.
Alpha decay of nucleus X:
A
ZX
Æ A-4Z-2Y + 42He
The helium nucleus atom is called alpha particle, sometimes 42α.
Beta decay of nucleus X, type 1: β - -decay
The most common type of beta decay is β- -decay where electrons are emitted as a neutron and
the X-nucleus turns into a proton and the emitted electron.
A
ZX
Æ AZ+1Y + 0-1e + 00ν
Where the ν indicates an antineutrino, a massless particle whose existence was postulated since
beta decay would violate the laws of momentum and energy conservation if X only split into Y and
the electron.
Beta decay of nucleus X, type 2 : β + -decay
Another type of beta decay is one where a positron, the antiparticle of the electron is emitted; a
particle with the same mass as the electron but the opposite electric charge. The third particle
emitted here is an ordinary neutrino, not an antineutrino.
A
ZX
Æ AZ-1Y + 0+1e + 00ν
Beta decay of nucleus X, type 3 : Electron capture (EC)
This is a case where the nucleus snatches an inner-shell electron. An ordinary neutrino, not an
antineutrino, is also emitted.
A
ZX
+ 0-1e Æ AZ-1Y + 00ν
Gamma decay of X
Gamma decay occurs when the nucleus is left in an excited state by a previous step. The excited
nucleus then emits a gamma photon when it relaxes. When the nucleus X has some of its parts in
a higher energy state than the lowest possible—when it is "excited"—is denoted with the symbol
X*.
A
*
ZX
Æ AZX + photon
Nuclear Fission
Nuclear fission is when an atomic nucleus splits into two or more pieces. This process is often
triggered by the absorption of a neutron. Nuclides that are capable of undergoing nuclear fission
are called fissile. When the nucleus splits, it also releases more neutrons and a large amount of
energy.
1
0n
236
91
142
1
+ 235
92 U→ 92 U→ 36 Kr + 56 Ba +3 0 n + energy
Krypton-91 and barium-142 are known as the fission fragments. A uranium-235 nucleus can split
in many different ways.
An enormous amount of energy is released during each fission reaction. In any fission reaction,
the combined mass of the incident neutron and the target nucleus is always greater than the
combined mass of the fission fragments and the released neutrons. Only about 0.1% of the mass
is converted into energy.
1
0
236
140
94
1
n + 235
92 U→ 92 U→ 54 Xe + 38 Sr +2 0 n + 160MeV
160MeV = 2.6*10-11J
Since the reaction produces two new neutrons, these can be used again to split new U-nuclei;
these can then split 4, 8, 16 and so on in an uncontrolled chain reaction (nuclear explosion). A
controlled chain reaction can be obtained if the number of neutrons on average can cause a
new fission = the multiplication factor =1.