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.

Z-charge 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.

Mass of 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:

radius of 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.

Elementary particles - 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

Nuclear particles - 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;

b) 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.


 mass deffect

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


or phosphorus



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):

Inelastic scattering:

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 several neutrons.

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

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 nuclear reactions.

Types of radioactivity:

1. α-decay.

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 biological effects.

Rule offset for α-decay:



2. β-decay.

a) Electronic-): the nucleus emits an electron and an electron antineutrino

b) positron (β+): the nucleus emits a positron and a neutrino

This 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 proton.

No electrons in the nucleus, they are formed as a result of the interconversion of the nucleons.
- a particle that is different from the electron only sign of the charge (+ e = 1.6 · 10-19 Cl).

From 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 βdecay


c) 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.

Generally, all 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

Nucleus 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 γ-condition

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 (max) 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.

therefore, 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.


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