Atomic nucleus
Daniel Vlk
Institute of Biophysics
Atomic nucleus
The particles forming the atomic nucleus – neutrons and
protons – are called nucleons.
They are attracted by the so-called strong interaction (one of
fundamental physical interactions: forces – gravitational,
electromagnetic, weak and strong).
Atomic (or proton) number Z – number of protons inside a
nucleus.
Neutron number N – number of neutrons inside a nucleus.
Atomic mass (or nucleon) number A – number of nucleons
inside a nucleus (A = Z + N).
Atomic nucleus
The general symbol for a nucleus should be written in following
form: ,where X is the chemical symbol of an element.
The electric charge of a nucleus is given by the number of its
protons:
Qnuc = Ze,
where e is the elementary charge (electric charge of one
electron or proton, 1.602×10-19 C).
XA
Z
Atomic nucleus
An element is a substance the nuclei of which are made up of
the same number of protons (number Z is the same in all the
nuclei).
A nuclide is a substance the nuclei of which are of identical
composition (numbers Z and N have the same values in all the
nuclei).
Isotopes are nuclides of an element the nuclei of which have the
same number Z but they differ in number of neutrons. Different
isotopes cannot be distinguished chemically because they
possess identical electron shells. They are of different mass, of
course. For example: carbon-12, carbon-14, uranium-235,
uranium-238 etc.
Atomic nucleus
Nuclear binding energy:
The nucleons are held together by the “strong interaction” (strong
nuclear force). The binding energy Enuc can be defined as the
energy which would be just necessary to disintegrate the nucleus
into individual nucleons.
During synthesis of nuclei from individual nucleons the same
amount of energy is liberated.
Atomic nucleus
Nuclear binding energy:
The nuclear binding energy per nucleon has different values for
different nuclides.
Maximum binding energy per nucleon (i.e. the highest stability)
can be found in nuclei which are in the middle part of the periodic
table of elements. The nucleus of the isotope (iron-56)
possesses the greatest value of binding energy; it means that
this nucleus is the most stable. Very light and very heavy nuclei
are not so stable which is a fact of extraordinary importance:
during synthesis of light elements (thermonuclear synthesis or
fusion) and splitting of heavy nuclei (nuclear fission) considerable
amount of nuclear energy are liberated.
Atomic nucleus
Nuclear binding energy:
Atomic nucleus
Nuclear binding energy:
The greater the binding energy the more stable is the nucleus.
This energy can be calculated from the difference Δm between
the mass of the nucleus mnuc, and the sum of masses of the
number of individual (free) protons and neutrons (mp, mn) which
are contained in the respective nucleus.
Δm = Zmp + Nmn – mnuc
Now it is possible to use Einstein’s formula of mass – energy
equivalence:
Eb = Δ mc2,
where Eb is the binding energy and Δm is the above defined
mass difference (mass defect).
Atomic nucleus
Nuclear binding energy:
Examples:
(thermonuclear synthesis of helium-3)
energy liberated: 5.49 MeV
(nuclear fission of uranium-235 induced by neutron)
energy liberated: about 200 MeV
Atomic nucleus
Nuclear reactor:
Is a complex device in which a controlled nuclear fission takes
place. Numerous rods made of uranium enriched by the isotope
are placed in a large steel container. A chain reaction is started
if a neutron interacts at low velocity (a moderated or thermal
neutron) with a nucleus of the isotope uranium-235, and causes
its fission. The two or three neutrons which are liberated by
fission are slowed down (decelerated) to be able to cause new
fission. The deceleration of neutrons is achieved by a moderator
(water, graphite or another substance composed of light nuclei).
Atomic nucleus
Nuclear reactor:
The fine regulation of neutron flux in the reactor is ensured by
insertion of control rods made of cadmium, for example. These
control rods reduce the number of neutrons able to induce
fission. The large amount of heat produced is utilized for heating
water or other suitable liquid in the primary loop of the reactor.
This very hot and more or less radioactive liquid warms up the
water in the secondary loop, which drives a powerful steam
turbine to produce electric energy. The neutron flux produced by
a nuclear reactor can be also used for production of artificial
radioactive elements – radionuclides.
Atomic nucleus
Natural and artificial radioactivity:
Radioactivity is the ability of a nucleus to emit particles or quanta
of energy. This process is also called radioactive decay or
disintegration.
Radioactive nuclides are called radionuclides (more than 1600
radionuclides have been identified in nature or prepared
artificially).
The radioactivity is accompanied by nuclear transformation. It
means that during the radioactive decay new (daughter) nuclei
arise.
Atomic nucleus
α (alpha)-radiation
Helium nuclei are emitted from a radionuclide. These particles
are electrically charged (+2e charge) and relatively heavy. They
cause direct ionization of ambient atoms, and all their energy is
transmitted to the medium along a very short track. It means that
this radiation is only little penetrating.
Scheme: A
ZX → A-4
Z-2Y + 4
2He
Example:
Atomic nucleus
β- (beta-minus)-radiation
Electrons are emitted from a radionuclide. One nuclear neutron is
transformed into a proton, an electron and a very light particle
called “electron antineutrino” (shown in the scheme and reaction
below).
Interaction of these particles with matter was described in the
paragraph dealing with the origin of X-rays. The ionization ability
of β-particles is relatively low hence their penetration into matter
is easier in comparison with a-particles.
Scheme: 1
0n → 1
1p + 0
1e- + 0
0ˉν + γ
A
ZX → A
Z+1Y + 0
1e-
Example:
Atomic nucleus
β+ (beta-plus)-radiation
Positrons are emitted from radionuclides. The positron is an
antiparticle of the electron. One nuclear proton is transformed
into a neutron, a positron and a very light particle called “positron
neutrino” (shown in the scheme and reaction below).
Scheme: 1
1p → 1
0n + 0
1e+ + 0
0ν + γ
A
ZX → A
Z-1Y + 0
1e+
Example:
Atomic nucleus
K - capture
Electron is captured from K shell by nucleus…
Scheme: 1
1p + 0
1e- → 1
0n + γ
A
ZX + 0
1e- → A
Z-1Y
Atomic nucleus
γ (gamma)-radiation
These high energy photons are emitted from a radionuclide. A
nucleus possessing some excess energy [*] emits a photon of
electromagnetic radiation. The γ-emission often accompanies
other types of radioactive decay. The ionization ability of this
radiation is relatively very low hence it penetrates very deeply
into matter. For interactions with matter, see the paragraphs
dealing with the photoelectric effect and Compton scatter.
Scheme: A
ZX* → A
ZX + γ
Example:
Atomic nucleus
Neutron radiation
A neutron is emitted from a radionuclide or can be liberated after
collision of two accelerated nuclei.
Example:
This nuclear reaction, followed by reaction
represents the first case of artificial radioactivity observed by
Frédéric and Irène Joliot-Curie in 1934.
The neutron ionizes matter indirectly. Fast neutrons transmit their
energy by impacts. This process is highly effective in collisions
with some light nuclei (such as hydrogen nucleus). Moderated
(slow, thermal) neutrons can enter inside some heavy nuclei
(such as uranium nucleus) and cause their disintegration –
fission.
Atomic nucleus
Proton radiation
Protons are emitted from a radionuclide, or liberated after
collision of two accelerated nuclei.
Example:
This nuclear reaction was the first case of artificial nuclear
transmutation (transformation). It was performed by Rutherford in
1919. Nitrogen was bombarded by α-particles.
All kinds of nuclear radiation, together with X-rays, are called
ionizing radiation because they are able to ionize atoms along
their tracks (trajectories) through matter. Chemical changes of
various substances or even damage to biological systems can be
caused in this way.
Radioactive transmutation law –
decay law
Radioactivity is a stochastic (probabilistic) process which can be
described in terms of probability. However, in great assemblies of
radioactive nuclei it can be also described by equations:
where At is the activity of a radioactive sample at time t = t, A0 is
the initial activity of the sample at time t = 0, Nt is the number of
nuclei left at time t = t, and the value N0 is the initial number of
radioactive nuclei at the time t = 0. λ is the decay (or
disintegration) constant [s-1] and t is the time of observation (i.e.
the time during which the individual radioactive decays were
counted).
t
t
t
t eNNoreAA λλ −−
== 00
Radioactive transmutation law –
decay law
Activity A of a radioactive emitter expresses the number of
decays (transmutations) in it per 1 second.
1 decay per 1 s = 1 Bq (becquerel) [s-1]
older unit of radioactivity is the curie, Ci, which was originally defined as "the quantity or
mass of radium emanation in equilibrium with one gram of radium (element)".
Today, 1 curie (Ci) = 3.7×1010 Bq
Half-life (time)
Half-life (time) T of a radionuclide is a quantity used for
characterization of the decay rate; it is better understandable
then the activity itself. It is the time during which the number of
radioactive nuclei (or the activity of a sample) decreases to one
half of the initial value. It is possible to derive (substitute Nt = NT
= N0/2 and t = T in the above formula) that
where λ is the decay constant.
λ
2ln
=T
Main applications of ionising radiation
and radionuclides
Attenuation of X-rays is utilized in medical imaging (radiography
and CT - computerized tomography) to show inner structures of
our body. g-radiation is used for this purpose in some other
imaging methods.
The strong biological effects of ionizing radiation (including killing
of tumour cells) is used in radiotherapy,
Heat production during nuclear fission is used for production of
electricity in the nuclear reactors.
Main applications of ionising radiation
and radionuclides
Chemical compounds (metabolites) labelled by radioisotopes
make it possible to follow metabolic pathways in living organisms
– these methods are called “tracing” techniques.
Measurement of the content of various radionuclides is often
used for dating of different organic and inorganic samples (e.g.,
radiocarbon method used in archaeology.