Nuclear physics. Properties and Structure of Atomic Nuclei
§ 1 The charge and mass of atomic nuclei
The most important features are nuclei is its core charge Z and mass M.
of the nucleus is determined by the number of positive elementary
charges concentrated in the nucleus. Of the positive elementary charge
p = 1.6021·10-19 Сl is the proton in the nucleus.
Atom as a whole is neutral and the charge of the nucleus determines both
the number of electrons in the atom. The distribution of electrons in
the atom for energy shells and subshells essentially depends on the
total number of the atom. Therefore, the nuclear charge to a large
extent determines the distribution of the electrons in an atom of their
states and the position of the element in the periodic system. Charge
of the nucleus is qn = z·e, where z - charge number of the nucleus equal to the ordinal number of the element in the periodic system.
the atomic nucleus is almost equal to the mass of the atom, because the
mass of the electrons of all atoms except hydrogen, is about 2.5·10-4 atomic mass. Atomic mass expressed in atomic mass units (amu). For amu adopted 1/12 the mass of a carbon atom .
1 amu. =1,6605655(86)·10-27 kg.
mN = ma - Z me.
Isotopes are called varieties of atoms of the chemical element, having the same charge, but different mass.
Nearest whole number to the atomic mass expressed in amu called the mass number and is denoted by the letter A. Identification of the chemical elements: A - mass number, X - symbol of a chemical element, Z-atomic number - number in the periodic table ():
Beryllium; Isotopes : , ', .
The radius of the nucleus:
where A - the mass number.
§2 Composition of the core
The nucleus of the hydrogen atom is called a proton.
mproton = 1,00783 amu , .
The scheme of the hydrogen atom.
In 1932, opened a particle called a neutron, which has a mass close to the mass of a proton (mneutron
= 1.00867 amu) and has no electrical charge. Then D.D. Ivanenko
conjectured proton-neutron structure of the nucleus: the nucleus
consists of protons and neutrons, and their sum is equal to the mass
number A. The charge number Z determines the number of protons in the nucleus, the neutron number N = A - Z.
- protons and neutrons in nuclei, have the common name of the
nucleons. Nucleons in nuclei are conditions that are significantly
different from their free states. Between nucleons are special nuclear
force. They say that the nucleon can be in two "charged states" -
proton with charge + e, and the neutron with a charge of 0.
§3 The binding energy of the nucleus. Mass defect. Nuclear forces
- protons and neutrons - are firmly held within the nucleus, so
between them are very large forces of attraction that can withstand the
huge forces of repulsion between like-charged protons. These special
forces due to the short distances between nucleons, called nuclear
forces. Nuclear forces are electrostatic (Coulomb).
The study of nuclei showed that the existing nuclear force between nucleons have the following features:
a) The short-range forces - is shown at distances of 10-15 m and decreases sharply with only a small increase in the distance;
nuclear forces do not depend on whether a particle (nucleon) charge -
charge independence of nuclear forces. Nuclear forces between neutrons
and protons, between two neutrons, the two protons are equal. Protons
and neutrons to the nuclear forces are the same.
The binding energy
is a measure of the stability of the nucleus. Nuclear binding energy
equal to the work you want to do for splitting the nucleus into its
constituent nucleons without informing them of the kinetic energy
МN < Σ(mp + mn)
MN - the core mass
Measurement of the core shows that the mass of the nucleus rest less than the sum of the rest masses of its constituent nucleons.
a measure of the binding energy is called the mass defect.
Einstein's equation in the special theory of relativity relates the energy and the rest mass of the particle.
In general, the binding energy of a nucleus can be calculated by the formula
where Z - atomic number (number of protons in the nucleus);
A - mass number (the total number of nucleons in the nucleus);
mp, mn and MN - mass of the proton, neutron and the nucleus
Mass defect (Δm) equal to 1 amu (amu - atomic mass unit) corresponds to the binding energy (Eb) of 1 a.u.e. (a.u.e. - atomic unit of energy) and equal 1a.m.u. · c2 = 931 MeV.
§4 Nuclear reactions
Changes in the nuclei during their interaction with the individual particles and with each other are called nuclear reactions.
There are the following, the most common nuclear reaction.
1. Reaction conversion.
In this case, the flown particle remains in the nucleus, but the
intermediate nucleus emits some other particle, so the kernel - the
product is different from the target nucleus.
2. Radiative capture reaction.
Gust particle stuck in the nucleus, but the excited nucleus emits
excess energy by emitting a γ-photon (used in nuclear reactors)
An example of the neutron capture reaction with cadmium
3. Scattering. Intermediate nucleus emits a particle identical
a gust, and can be:
• elastic scattering, in which ;
• inelastic scattering in which.
Elastic scattering of neutrons by carbon (used in reactors to slow down neutrons):
4. Fission reaction.
It is a response that comes always with energy release. It is the
basis for the technical production and use of nuclear energy. When
fission excitation intermediate compound nucleus is so large that it
is divided into two approximately equal fragments, with the release of
If the excitation energy
is low, there is no division of the nucleus, and the nucleus, losing
the excess energy by emitting γ - photon or neutron, will return to
normal (Fig. 1). But if introduced neutron energy is high, the excited
nucleus starts to deform, it is formed as a result of the neck and it
is divided into two fragments, flying at high speed, with two neutrons
emitted (Fig. 2).
Chain reaction -
self-propagating fission reaction. To carry out its necessary that of
the secondary neutrons produced in a fission event, at least one could
cause the next fission (as some neutrons can participate in reactions
capture without causing division). Quantitatively, the condition of
existence of a chain reaction expresses the multiplication factor
k < 1 - a chain reaction is impossible, k = 1 (m = mcr) - a chain reaction with a fixed number of neutrons (in a nuclear reactor}, k> 1 (m > mcr) - nuclear bombs.
§1 The natural radioactivity
is the spontaneous conversion of an unstable nucleus of one element
into the other core element. Natural radioactivity is called
radioactivity observed in the naturally occurring unstable isotopes.
Artificial radioactive isotopes called radioactivity produced by
Types of radioactivity:
The emission of
the nuclei of some chemical elements α-system of two protons and two
neutrons are connected together (a-particle - a helium nucleus
α-decay inherent in heavy nuclei with A > 200 and Z
> 82. When going to the substance of α-particles produce on its
way strong ionization of atoms (ionization - separation of electrons
from an atom), acting upon them an electric field. The distance by which
the flies α-particle in matter before its full stop, called mileage
or penetrating ability particles (denoted by R, [R] =
m, cm). . Under normal conditions, α-particles are formed in the air
30,000 pairs of ions per 1 cm path. Specific ionization is the number
of ion pairs formed by 1 cm path length. α-particle has a strong
Rule offset for α-decay:
a) Electronic (β-): the nucleus emits an electron and an electron antineutrino
b) positron (β+): the nucleus emits a positron and a neutrino
process occurs through the conversion of one form of the nucleon in
the nucleus to another: a neutron into a proton into a neutron or a
No electrons in the nucleus, they are formed as a result of the interconversion of the nucleons.
Positron - a particle that is different from the electron only sign of the charge (+ e = 1.6 · 10-19 Cl).
the experiment that when β - decay of isotopes lose the same amount
of energy. Consequently, on the basis of the law of conservation of
energy Pauli predicted that ejected another light particle, called an
antineutrino. Antineutrino has no charge and mass. Energy losses β -
particles as they pass through the substance are caused mainly by
ionization. Some of the energy is lost to the X-ray emission during
braking β - particles by nuclei of the absorbing substance. Since β -
the particles have a small mass, a single charge and a very high
velocity, their capacity of ionizing small (100 times smaller than
that of α - particles), therefore, penetrating capability (mileage) of
β - particles substantially greater than in α - particles.
Rβ air = 200 m, Rβ Pb ≈ 3 mm.
β-- decay occurs in natural and artificial radioactive nuclei. β+ - only artificial radioactivity.
Rule offset β—decay
K - capture (electron capture) - nucleus absorbs one of the electrons
at the K shell (or more rarely L or M) of its atom, resulting in one of
the protons becomes a neutron, thereby emitting neutrinos
Scheme K - capture:
Place in the electron shell, release of captured electrons, electrons filled from the upper layers, whereby there are X-rays.
3. γ -rays.
types of radioactivity are accompanied by the emission of γ-rays.
γ-rays - is electromagnetic radiation having wavelengths ranging from
one to a few hundredths of angstroms λ’=~ 1- 0.01 Å=10-10-10-12m energy γ-rays reaches millions of eV.
Wγ ~ MeV
1 eV = 1.6·10-19J
experiencing radioactive decay, as a rule, is excited and his
transition to the ground state is accompanied by the emission of γ -
the photon. Thus the energy of the photon is determined by the
where Е2 and E1-energy core.
Е2 is the energy of the excited state;
E1 - the energy of the ground state.
Absorption of γ-rays substance is caused by three main processes:
1) photoelectric effect (for hv < 1 MeV);
2) the formation of electron - positron pairs;
3) scattering (Compton effect) –
Absorption of γ-rays is on the Bouguer’s law:
where μ - linear attenuation coefficient that depends on the energy γ - rays and the properties of the medium;
І0-intensity of the incident parallel beam;
І - intensity of the beam after the passage of thickness x cm.
γ-rays - one of the most penetrating radiation. For most stringent rays (hνmax) thickness equal to half the absorption; for lead 1.6 cm, the iron - 2.4 cm, aluminum - 12 cm, ground - 15 cm
§2 the Basic Law of radioactive decay.
The number of broken of nuclei dN is proportional to the initial number of nuclei N and decay time dt, dN ~ N dt. The Basic Law of radioactive decay in the differential form:
The coefficient λ is called the decay constant for this type of cores. The "-" means that dN must be negative, since a finite number of broken nuclei less than the initial one.
λ characterizes the proportion of nuclei decay per unit time, i.e.
determines the rate of radioactive decay. λ does not depend on
external conditions, and is determined only by the intrinsic properties
of the nuclei. [λ] = s-1.
The Basic Law of radioactive decay in the integral form
where N 0 - initial number of radioactive nuclei at t = 0;
N - the number is not broken nuclei in time t;
λ - the radioactive decay constant.
The rate of decay in practice is judged not by using λ, but Т1/2 - half-life - the time in which half of the decays of the initial number of nuclei. Relationship Т1/2 and λ
Т1/2 U238 = 4.5·106 years, Т1/2 Ra = 1590 years, Т1/2 Rn = 3.825 days. The number of decays per unit time А = - dN/dt is called active part of the radioactive substance.
[A] = 1 Bq (Becquerel)= 1 decay / 1s;
[A] = 1 Ci = 1 Curie = 3.7·1010 Bq.
Law changes in activity
where А0 =λN0 - initial activity at time t = 0;
A - activity at time t.