Binding energy of an atomic nucleus: formula, meaning and definition. The mass defect of atomic nuclei. Communication energy
Absolutely anyone chemical consists of a specific set of protons and neutrons. They are held together due to the fact that the binding energy of the atomic nucleus is present inside the particle.
A characteristic feature of nuclear gravitational forces is their very high power at relatively small distances (from about 10 -13 cm). As the distance between the particles grows, the forces of attraction inside the atom also weaken.
Reasoning about the binding energy inside the nucleus
If we imagine that there is a way to separate protons and neutrons from the atomic nucleus in turn and to place them at such a distance that the binding energy of the atomic nucleus ceases to act, then this must be very hard work. In order to extract its constituents from the nucleus of an atom, one must try to overcome the intra-atomic forces. These efforts will go into splitting the atom into its contained nucleons. Therefore, it can be judged that the energy of an atomic nucleus is less than the energy of the particles of which it is composed.
Is the mass of intra-atomic particles equal to the mass of an atom?
Already in 1919, researchers learned how to measure the mass of an atomic nucleus. Most often it is "weighed" with the help of special technical devices, which are called mass spectrometers. The principle of operation of such devices is that the characteristics of the motion of particles with different masses are compared. Moreover, such particles have the same electric charges. Calculations show that those particles that have different indicators masses move along different trajectories.
Modern scientists have found out with great accuracy the masses of all nuclei, as well as their constituent protons and neutrons. If we compare the mass of a particular nucleus with the sum of the masses of the particles contained in it, it turns out that in each case the mass of the nucleus will be greater than the mass of individual protons and neutrons. This difference will be approximately 1% for any chemical. Therefore, we can conclude that the binding energy of an atomic nucleus is 1% of its rest energy.
Properties of intranuclear forces
The neutrons that are inside the nucleus are repelled from each other by Coulomb forces. But at the same time, the atom does not fall apart. This is facilitated by the presence of an attractive force between the particles in the atom. Such forces, which have a nature other than electrical, are called nuclear. And the interaction of neutrons and protons is called strong interaction.
Briefly, the properties of nuclear forces boil down to the following:
- it is charge independence;
- action only over short distances;
- and also saturation, which is understood as keeping only a certain number of nucleons near each other.
According to the law of conservation of energy, at the moment when nuclear particles combine, energy is released in the form of radiation.
Binding energy of atomic nuclei: formula
For the calculations mentioned, the generally accepted formula is used:
E sv= (Z m p + (A-Z) m n -MI am) · C²
Here under E sv the binding energy of the nucleus is understood; with- the speed of light; Z-number of protons; (A-Z) is the number of neutrons; m p denotes the mass of a proton; a m n is the neutron mass. M i denotes the mass of the nucleus of an atom.
Internal energy of the nuclei of various substances
The same formula is used to determine the binding energy of a nucleus. The bond energy calculated by the formula, as previously indicated, is no more than 1% of total energy atom or energy of rest. However, upon closer examination, it turns out that this number fluctuates quite strongly when going from substance to substance. If we try to determine its exact values, then they will be especially different for the so-called light nuclei.
For example, the binding energy inside a hydrogen atom is zero because there is only one proton in it. The binding energy of a helium nucleus will be 0.74%. For the nuclei of a substance called tritium, this number will be equal to 0.27%. Oxygen has 0.85%. In nuclei, where there are about sixty nucleons, the intra-atomic bond energy will be about 0.92%. For atomic nuclei with a greater mass, this number will gradually decrease to 0.78%.
To determine the binding energy of the nucleus of helium, tritium, oxygen, or any other substance, the same formula is used.
Types of protons and neutrons
The main reasons for these differences can be explained. Scientists have found that all the nucleons that are contained within the nucleus are divided into two categories: surface and internal. Internal nucleons are those that are surrounded by other protons and neutrons on all sides. The superficial ones are surrounded by them only from the inside.
The binding energy of an atomic nucleus is a force that is more pronounced in internal nucleons. Something similar, by the way, occurs with the surface tension of various liquids.
How many nucleons fit in the nucleus
It was found that the number of internal nucleons is especially small in the so-called light nuclei. And in those that belong to the category of the lightest, almost all nucleons are regarded as surface. It is believed that the binding energy of an atomic nucleus is a quantity that should increase with the number of protons and neutrons. But even this growth cannot continue indefinitely. At a certain amount nucleons - and this is from 50 to 60 - another force comes into action - their electrical repulsion. It occurs even regardless of the presence of binding energy inside the nucleus.
The binding energy of the atomic nucleus in various substances used by scientists to release nuclear energy.
Many scientists have always been interested in the question: where does energy come from when lighter nuclei merge into heavy ones? Actually, this situation is similar to atomic fission. In the process of fusion of light nuclei, just as it happens in the splitting of heavy nuclei, nuclei of a stronger type are always formed. To "get" from light nuclei all the nucleons in them, it is required to spend less quantity energy, rather than what is released when they combine. The converse is also true. In fact, the fusion energy, which falls on a certain unit of mass, may be greater than the specific fission energy.
Scientists who investigated the processes of nuclear fission
The process was discovered by scientists Hahn and Strassmann in 1938. Within the walls of the Berlin University of Chemistry, researchers discovered that in the process of bombarding uranium with other neutrons, it turns into lighter elements in the middle of the periodic table.
A significant contribution to the development of this field of knowledge was also made by Lisa Meitner, whom Hahn suggested at one time to study radioactivity together. Hahn allowed Meitner to work only on the condition that she would conduct her research in the basement and never climb upper floors that was a fact of discrimination. However, this did not prevent her from achieving significant success in studies of the atomic nucleus.
Since the nucleons in the nucleus are bound by nuclear forces, it takes a lot of energy to separate the nucleus into its constituent protons and neutrons. The same energy is released if free protons and neutrons combine to form a nucleus. This energy is called the binding energy of the nucleus. According to Einstein's theory of relativity, energy corresponds to mass. Therefore, the mass of the nucleus should be less than the sum of the masses of its constituent free protons and neutrons. The difference between the sum of the rest masses of free protons and neutrons from which the nucleus is formed and the mass of the nucleus is called nuclear mass defect... The binding energy is equal to: E sv = WITH 2 × D m
D m Is the defect in the mass of the nucleus.
The binding energy is expressed in megaelectronvolts (MeV) (MeV = 10 6 EV). Since the atomic mass unit (amu) is 1.66 × 10 -27 kg, the corresponding energy can be determined:
Using a mass spectrograph, the masses of all isotopes were measured and the values of the mass defect and binding energy were calculated for all nuclei, which are used to calculate nuclear reactions. If in some reaction nuclei and particles are obtained whose total mass is less than that of the initial nuclei and particles, then in such reactions energy is released; if more, then it is absorbed and such a reaction will not occur spontaneously.
Let's carry out an energy calculation of the nuclear reaction of the transformation of radium into radon: 
... The binding energy of the initial nucleus is 1731.6 MeV, and the total binding energy of the formed nuclei is 1708.2 + 28.3 = 176.5 MeV and is higher than the binding energy of the initial nucleus by 4.9 MeV. Consequently, in this reaction, an energy of 4.9 MeV is released, which is mainly kinetic energy g-particles.
Great importance has a binding energy per 1 nucleon. The larger it is, the stronger the core. Strongest medium cores. Light nuclei do not use their binding energies enough. Heavy nuclei are weakened by Coulomb repulsive forces, which, unlike nuclear ones, act between all nucleons of the nucleus. An important conclusion follows from this: energy is released when middle nuclei are formed. This can be when dividing a heavy nucleus into two medium ones in nuclear reactors or in the synthesis of the middle nucleus from two lighter ones. These are thermonuclear fusion reactions occurring in the sun and stars.
TASKS FOR BLOCK 25
1. What does the thorium isotope turn into, the nucleus of which undergoes three consecutive a decays.
Solution:
When an a-particle is emitted, the nuclear charge decreases by 2 units, and the mass number by 4 units, which means that when 3 a-particles are emitted, the nuclear charge decreases by 2 × 3 = 6 units, and the mass number by 4 × 3 = 12 units and then we get an isotope according to the table, we find that it is polonium or 
2. When nitrogen is bombarded with neutrons, two isotopes are formed, one of which is an isotope of hydrogen The isotope of which element is formed during this nuclear reaction.
V in this case a nuclear reaction occurs with the production of an unknown isotope X.
In nuclear reactions, the number of nucleons and charge are conserved, therefore the sum of the subscripts and superscripts is constant.
According to the periodic table, we find that carbon is obtained:
Thus: 
3.
To add a nuclear reaction: 
We determine that the unknown particle has a charge number of 1 and a mass number of 1, which means that an isotope of hydrogen, i.e. proton, i.e. we have: 
4. Find the energy corresponding to 1 amu. Express it in MeV.
Solution:
E = m c 2
m= 1 amu = 1.66 × 10 -27 kg
WITH= 3 × 10 8 m / s
E= 1.66 × 10 -27 × (3 × 10 8) 2 = 14.94 × 10 -11 J
1 EV = 1.6 × 10 -19 J
This means: 1 amu. corresponds to 931 MeV.
5. Calculate the energy of a tritium nucleus if the mass of a proton is m p= 1.00814 amu, neutron mass m n= 1.00898 and the mass of the tritium atom A= 3.01700 amu
Given:
m p= 1.00814 amu
m n = 1,00898
A = 3.01700 amu
__________________
E sv – ?
Solution:
Tritium nucleus: consists of one proton and two neutrons, the total mass of which is: m p + 2m n = 1.00814 + 2 × 1.00898 = = 3.02610
The mass defect means:
D m= 3.02610 - 3.01700 amu = 0.00910 amu
since 1 amu - 931 MeV; then E sv= 931 × D m or
E sv= 931 × 0.00910 (MeV) = 8.5 MeV
Answer: 8.5 MeV
6. Energy is released or absorbed during the reaction:
It was possible to calculate the binding energy of each nucleus, but you can also use a special table:
The total mass of nuclei and particles before the reaction: 39.2 + 28.3 = 67.5 MeV
after reaction: 64.7 + 0 = 64.7 MeV
This means that energy is absorbed in such a reaction: 67.5 - 64.7 = 2.8 MeV
7.
Determine the reaction energy: 
before reaction: 2.2 + 2.2 = 4.4 MeV
after reaction: 8.5 MeV
energy released: 8.5 - 4.4 = 4.1 MeV
8. There is 4 g of radioactive cobalt. How many grams of cobalt decays in 216 days if its half-life is 72 days?
Given:
m 0 = 4g
t= 216 days
T= 72 days
D m – ?
Solution:
Since the mass of a substance is directly proportional to the number of atoms, then: DN = N 0 - N;
Means: 
Means: and
Answer: 3.5 g.
9. There is 8 kg of radioactive cesium. Determine the mass of non-decayed cesium after 135 years of radioactive decay, if its half-life is 27 years.
Until recently, people believed that an atom is a whole, indivisible particle. Later it became clear that it consists of a nucleus and electrons revolving around it. At the same time, the central part was again considered indivisible and integral. Today we know that it is composed of protons and neutrons. Moreover, depending on the number of the latter, the same substance may have several isotopes. So, tritium is a substance, how to get it and use it?
Tritium - what is it?
Hydrogen is the simplest substance in nature. If we talk about its most common form, which will be discussed in more detail below, then its atom consists of only one proton and one electron. However, it can also accept "extra" particles, which somewhat change its properties. So, the tritium nucleus consists of a proton and two neutrons. And if protium, that is the most simple form hydrogen - this cannot be said about its "improved" version - in nature it is found in insignificant quantities.
The hydrogen isotope tritium (the name comes from the Greek word for "third") was discovered in 1934 by Rutherford, Oliphant and Hartek. And in fact, they tried to find him for a very long time and persistently. Immediately after the discovery of deuterium and heavy water in 1932, scientists began to search for this isotope by increasing the sensitivity when studying ordinary hydrogen. However, in spite of everything, their attempts were in vain - even in the most concentrated samples it was not possible to get even a hint of the presence of a substance that simply had to exist. But in the end, the search was still crowned with success - Oliphant synthesized the element with the help of Rutherford's laboratory.
In short, the definition of tritium is as follows: a radioactive isotope of hydrogen, the nucleus of which consists of a proton and two neutrons. So what is known about him?
About hydrogen isotopes
The first element of the periodic table is at the same time the most common in the universe. Moreover, in nature, it occurs in the form of one of its three isotopes: protium, deuterium or tritium. The first nucleus consists of one proton, which gave it its name. By the way, this is the only stable element that lacks neutrons. The next in the series of hydrogen isotopes is deuterium. The nucleus of its atom consists of a proton and a neutron, and the name goes back to the Greek word for "second".
The laboratory also obtained even heavier isotopes of hydrogen with mass numbers from 4 to 7. Their half-life is limited to fractions of a second.
Properties
The atomic mass of tritium is approximately 3.02 amu. e. m. by their own physical properties this substance is almost indistinguishable from ordinary hydrogen, that is, in normal conditions is a light gas without color, taste and smell, has a high thermal conductivity. At a temperature of about -250 degrees Celsius, it becomes a light and flowing colorless liquid. The range within which it is in a given state of aggregation is rather narrow. The melting point is about 259 degrees Celsius, below which hydrogen becomes a snow-like mass. In addition, this element is fairly soluble in some metals.
However, there are also some differences in properties. Firstly, the third isotope is less reactive, and secondly, tritium is radioactive and therefore unstable. is just over 12 years old. In the process of radiolysis, it turns into the third isotope of helium with the emission of an electron and an antineutrino.
Receiving
In nature, tritium is found in small amounts and is most often formed in upper layers atmosphere in the collision of cosmic particles and, for example, nitrogen atoms. However, there is also industrial method obtaining this element by irradiating lithium-6 with neutrons in
It costs about $ 30 million to synthesize tritium in a volume of about 1 kilogram.
Usage
So, we learned a little more about tritium - what it is and its properties. But why is it needed? Let's figure it out a little below. According to some data, the world commercial demand for tritium is about 500 grams per year, and about 7 kilograms is spent on military needs.
According to the American Institute for Energy Research and environment, from 1955 to 1996, 2.2 centners of superheavy hydrogen were produced in the USA. And for 2003, the total stocks of this element were about 18 kilograms. What are they used for?
First, tritium is necessary to maintain the combat capability of nuclear weapons, which, as you know, are still possessed by some countries. Secondly, thermonuclear power engineering cannot do without it. Tritium is also used in some scientific research, for example, in geology, natural waters are dated with its help. Another purpose is to power the watch backlight. In addition, experiments are currently underway to create ultra-low-power radioisotope generators, for example, to power autonomous sensors. In this case, it is expected that their service life will be about 20 years. The cost of such a generator will be about one thousand dollars.
As original souvenirs there are also keychains with small amount tritium inside. They give off a glow and look quite exotic, especially if you know about the inner content.
Danger
Tritium is radioactive, which explains some of its properties and uses. Its half-life is about 12 years, while helium-3 is formed with the emission of an antineutrino and an electron. In the process of this reaction, 18.59 kW of energy is released and beta particles are distributed in the air. It may seem strange to the layman that a radioactive isotope is used, say, for the backlight in a watch, because it can be dangerous, isn't it? In fact, tritium hardly threatens human health with anything, since beta particles in the process of its decay spread to a maximum of 6 millimeters and cannot overcome the simplest obstacles. However, this does not mean that working with it is absolutely safe - any ingestion with food, air or absorption through the skin can lead to problems. While it clears easily and quickly in most cases, this is not always the case. So tritium - what is it in terms of radiation hazard?
Protective measures
Although low energy the decay of tritium prevents radiation from spreading seriously, so that beta particles cannot even penetrate the skin, do not neglect your health. When working with this isotope, you can, of course, not use a radiation protection suit, but elementary rules, such as closed clothing and surgical gloves must be observed. Since tritium is the main hazard when ingested, it is important to suppress activities that would make it possible. Otherwise, nothing to worry about.
If, nevertheless, he is in a large number entered into the tissues of the body, may develop, acute or chronic radiation sickness, depending on the duration, dose and regularity of exposure. In some cases, this ailment is successfully cured, but with extensive lesions, a lethal outcome is possible.
In any normal body there are traces of tritium, although they are absolutely insignificant and hardly affect. Well, for lovers of watches with luminous hands, its level is several times higher, although it is still considered safe.
Super heavy water
Tritium, like ordinary hydrogen, can form new substances. In particular, it is included in the so-called superheavy (superheavy) water molecule. The properties of this substance are not too different from the usual H 2 O for every person. Despite the fact that tritium water can also participate in metabolism, it has a rather high toxicity and is excreted within a ten-day period, during which tissues can get quite high degree irradiation. And although this substance is less dangerous in itself, it is more dangerous due to the period during which it is in the body.