Atomic mass is the sum of the masses of all protons, neutrons and electrons that make up an atom or molecule. Compared to protons and neutrons, the mass of electrons is very small, so it is not taken into account in calculations. Although this is not formally correct, the term is often used to refer to the average atomic mass of all isotopes of an element. This is actually relative atomic mass, also called atomic weight element. Atomic weight is an average atomic masses all isotopes of an element found in nature. Chemists must differentiate between these two types of atomic mass when doing their work—an incorrect atomic mass value can, for example, result in an incorrect result for the yield of a reaction.
Steps
Finding atomic mass from the periodic table of elements
- The atomic mass unit characterizes the mass one mole of a given element in grams. This value is very useful in practical calculations, since it can be used to easily convert the mass of a given number of atoms or molecules of a given substance into moles, and vice versa.
-
Find the atomic mass in the periodic table. Most standard periodic tables contain the atomic masses (atomic weights) of each element. Typically, they are listed as a number at the bottom of the element cell, below the letters representing the chemical element. Usually this is not a whole number, but a decimal fraction.
Remember that the periodic table gives the average atomic masses of elements. As noted earlier, the relative atomic masses given for each element in the periodic table are the average of the masses of all isotopes of the atom. This average value is valuable for many practical purposes: for example, it is used in calculating the molar mass of molecules consisting of several atoms. However, when you are dealing with individual atoms, this value is usually not enough.
- Since the average atomic mass is an average of several isotopes, the value shown in the periodic table is not accurate the value of the atomic mass of any single atom.
- The atomic masses of individual atoms must be calculated taking into account the exact number of protons and neutrons in a single atom.
Calculation of the atomic mass of an individual atom
-
Find the atomic number of a given element or its isotope. The atomic number is the number of protons in the atoms of an element and never changes. For example, all hydrogen atoms, and only they have one proton. The atomic number of sodium is 11 because it has eleven protons in its nucleus, while the atomic number of oxygen is eight because it has eight protons in its nucleus. You can find the atomic number of any element in the periodic table - in almost all its standard versions, this number is indicated above the letter designation chemical element. The atomic number is always a positive integer.
- Suppose we are interested in the carbon atom. Carbon atoms always have six protons, so we know that its atomic number is 6. In addition, we see that in the periodic table, at the top of the cell with carbon (C) is the number "6", indicating that the atomic carbon number is six.
- Note that the atomic number of an element is not uniquely related to its relative atomic mass in the periodic table. Although, especially for the elements at the top of the table, it may appear that an element's atomic mass is twice its atomic number, it is never calculated by multiplying the atomic number by two.
-
Find the number of neutrons in the nucleus. The number of neutrons can be different for different atoms of the same element. When two atoms of the same element with the same number of protons have different numbers of neutrons, they are different isotopes of that element. Unlike the number of protons, which never changes, the number of neutrons in the atoms of a given element can often change, so the average atomic mass of an element is written as a decimal fraction with a value lying between two adjacent whole numbers.
Add up the number of protons and neutrons. This will be the atomic mass of this atom. Ignore the number of electrons that surround the nucleus - their total mass is extremely small, so they have virtually no effect on your calculations.
Calculating the relative atomic mass (atomic weight) of an element
-
Determine which isotopes are contained in the sample. Chemists often determine the isotope ratios of a particular sample using a special instrument called a mass spectrometer. However, in training, this data will be provided to you in assignments, tests, and so on in the form of values taken from the scientific literature.
- In our case, let's say that we are dealing with two isotopes: carbon-12 and carbon-13.
-
Determine the relative abundance of each isotope in the sample. For each element, different isotopes occur in different ratios. These ratios are almost always expressed as percentages. Some isotopes are very common, while others are very rare—sometimes so rare that they are difficult to detect. These values can be determined using mass spectrometry or found in a reference book.
- Let's assume that the concentration of carbon-12 is 99% and carbon-13 is 1%. Other isotopes of carbon really exist, but in quantities so small that in this case they can be neglected.
-
Multiply the atomic mass of each isotope by its concentration in the sample. Multiply the atomic mass of each isotope by its percentage abundance (expressed as a decimal). To convert interest to decimal, simply divide them by 100. The resulting concentrations should always add up to 1.
- Our sample contains carbon-12 and carbon-13. If carbon-12 makes up 99% of the sample and carbon-13 makes up 1%, then multiply 12 (the atomic mass of carbon-12) by 0.99 and 13 (the atomic mass of carbon-13) by 0.01.
- The reference books give percentages based on the known quantities of all isotopes of a particular element. Most chemistry textbooks contain this information in a table at the end of the book. For the sample being studied, the relative concentrations of isotopes can also be determined using a mass spectrometer.
-
Add up the results. Sum up the multiplication results you got in the previous step. As a result of this operation, you will find the relative atomic mass of your element - the average value of the atomic masses of the isotopes of the element in question. When an element as a whole is considered, rather than a specific isotope of a given element, this value is used.
- In our example, 12 x 0.99 = 11.88 for carbon-12, and 13 x 0.01 = 0.13 for carbon-13. The relative atomic mass in our case is 11.88 + 0.13 = 12,01 .
- Some isotopes are less stable than others: they break down into atoms of elements with fewer protons and neutrons in the nucleus, releasing particles that make up the atomic nucleus. Such isotopes are called radioactive.
Learn how atomic mass is written. Atomic mass, that is, the mass of a given atom or molecule, can be expressed in standard SI units - grams, kilograms, and so on. However, because atomic masses expressed in these units are extremely small, they are often written in unified atomic mass units, or amu for short. – atomic mass units. One atomic mass unit is equal to 1/12 the mass of the standard isotope carbon-12.
§1 Charge and mass of atomic nuclei
The most important characteristics of a nucleus are its charge and mass M.
Z- the charge of the nucleus is determined by the number of positive elementary charges concentrated in the nucleus. Carrier of positive elementary charge R= 1.6021·10 -19 C in the nucleus is a proton. The atom as a whole is neutral and the charge of the nucleus simultaneously determines the number of electrons in the atom. The distribution of electrons in an atom across energy shells and subshells significantly depends on their total number in the atom. Therefore, the nuclear charge largely determines the distribution of electrons among their states in the atom and the position of the element in the Mendeleev periodic table. The nuclear charge isqI = z· e, Where z-charge number of the nucleus, equal to the atomic number of the element in the periodic system.
The mass of the atomic nucleus practically coincides with the mass of the atom, because the mass of the electrons of all atoms, except hydrogen, is approximately 2.5·10 -4 the mass of the atoms. The mass of atoms is expressed in atomic mass units (amu). For a.u.m. assumed to be 1/12 the mass of a carbon atom.
1 amu =1.6605655(86)·10 -27 kg.
mI = m a - Z m e.
Isotopes are varieties of atoms of a given chemical element that have the same charge but differ in mass.
The integer closest to the atomic mass expressed in a.u. m . called mass number m and denoted by the letter A. Chemical element designation: A - mass number, X is the symbol of the chemical element,Z-charge number - serial number in the periodic table ():
Beryllium; Isotopes: , ", .
Core radius:
where A is the mass number.
§2 Composition of the core
Nucleus of a hydrogen atomcalled proton
mproton= 1.00783 amu , 
.
Hydrogen atom diagram
In 1932, a particle called a neutron was discovered, with a mass close to the mass of a proton (mneutron= 1.00867 a.m.u.) and without electric charge. Then D.D. Ivanenko formulated a hypothesis about the proton-neutron structure of the nucleus: the nucleus consists of protons and neutrons and their sum is equal to the mass number A. 3rd serial numberZdetermines the number of protons in the nucleus, the number of neutronsN =A - Z.
Elementary particles - protons and neutrons included into the core, got common name nucleons. The nucleons of nuclei are in states, significantly different from their free states. Between nucleons there is a special I de r new interaction. They say that a nucleon can be in two “charge states” - a proton with a charge+ e, And neutron with charge 0.
§3 Nuclear binding energy. Mass defect. Nuclear forces
Nuclear particles - protons and neutrons - are firmly held inside the nucleus, so very strong attractive forces act between them, capable of resisting the enormous repulsive forces between similarly charged protons. These special forces that arise at small distances between nucleons are called nuclear forces. Nuclear forces are not electrostatic (Coulomb).
The study of the nucleus has shown that the nuclear forces acting between nucleons have the following features:
a) these are short-range forces - manifesting themselves at distances of the order of 10 -15 m and sharply decreasing even with a slight increase in distance;
b) nuclear forces do not depend on whether the particle (nucleon) has a charge - over-row independence of nuclear forces. The nuclear forces acting between a neutron and a proton, between two neutrons, and between two protons are equal. The proton and neutron are the same in relation to nuclear forces.
Binding energy is a measure of the stability of the atomic nucleus. The binding energy of a nucleus is equal to the work that must be done to split a nucleus into its constituent nucleons without imparting kinetic energy to them
M I< Σ( m p + m n)
Mya - core mass
Measurement of nuclear masses shows that the rest mass of a nucleus is less than the sum of the rest masses of its constituent nucleons.
Magnitude
serves as a measure of binding energy and is called mass defect.
Einstein's equation in special relativity relates the energy and rest mass of a particle.
In general, the binding energy of a nucleus can be calculated using the formula
Where Z - charge number (number of protons in the nucleus);
A- mass number (total number of nucleons in the nucleus);
m p, , m n And M I- mass of proton, neutron and nucleus
Mass defect (Δ m) equal to 1 a.u. m. (a.u. - atomic mass unit) corresponds to a binding energy (Eb) equal to 1 a.u.u. (a.u.e. - atomic unit of energy) and equal to 1 a.u.m.·s 2 = 931 MeV.
Changes in nuclei when they interact with individual particles and with each other are usually called nuclear reactions.
The following are the most common nuclear reactions.
- Transformation reaction . In this case, the incident particle remains in the nucleus, but the intermediate nucleus emits some other particle, so the product nucleus differs from the target nucleus.
- Radiative capture reaction . The incident particle gets stuck in the nucleus, but the excited nucleus emits excess energy by emitting a γ-photon (used in the operation of nuclear reactors)
An example of a neutron capture reaction by cadmium
or phosphorus
- Scattering. The intermediate nucleus emits a particle identical
with an attack, and it could be:
Elastic scattering neutrons with carbon (used in reactors to moderate neutrons):
Inelastic scattering :
- Fission reaction. This is a reaction that always occurs with the release of energy. It is the basis for the technical production and use of nuclear energy. During a fission reaction, the excitation of the intermediate compound nucleus is so great that it splits into two approximately equal fragments, releasing several neutrons.
If the excitation energy is low, then the division of the nucleus does not occur, and the nucleus, having lost excess energy by emitting a γ - photon or neutron, will return to its normal state (Fig. 1). But if the energy contributed by the neutron is high, then the excited nucleus begins to deform, a waist forms in it and, as a result, it splits into two fragments that fly apart at enormous speeds, and two neutrons are emitted
(Fig. 2).
Chain reaction- self-developing fission reaction. To implement it, it is necessary that of the secondary neutrons formed during one fission act, at least one can cause the next fission act: (since some neutrons can participate in capture reactions without causing fission). Quantitatively, the condition for the existence of a chain reaction expresses reproduction rate
k < 1 - цепная реакция невозможна, k = 1 (m = m cr ) - chain reactions with a constant number of neutrons (in a nuclear reactor),k > 1 (m > m cr ) - nuclear bombs.
§1 Natural radioactivity
Radioactivity is the spontaneous transformation of unstable nuclei of one element into the nuclei of another element. Natural radioactivity is called radioactivity observed in unstable isotopes existing in nature. Artificial radioactivity is the radioactivity of isotopes obtained as a result of nuclear reactions.
Types of radioactivity:
- α-decay.
The emission by the nuclei of some chemical elements of the α-system of two protons and two neutrons connected together (a-particle is the nucleus of a helium atom)
α-decay is inherent heavy nuclei With A> 200 andZ > 82. When moving through matter, α-particles produce strong ionization of atoms along their path (ionization is the separation of electrons from an atom), acting on them with their electric field. The distance an alpha particle travels in a substance before it stops completely is called particle path or penetrating power(denotedR, [R] = m, cm). . Under normal conditions, an α particle forms V air 30,000 pairs of ions per 1 cm of path. Specific ionization is the number of ion pairs formed per 1 cm of path length. The α-particle has a strong biological effect.
Bias rule for α decay:
2. β-decay.
a) electron (β -): the nucleus emits an electron and an electron antineutrino
b) positron (β +): the nucleus emits a positron and neutrino
This process occurs by converting one type of nucleon in a nucleus into another: a neutron into a proton or a proton into a neutron.
There are no electrons in the nucleus; they are formed as a result of the mutual transformation of nucleons.
Positron - a particle that differs from an electron only in the sign of its charge (+e = 1.6·10 -19 C)
From the experiment it follows that during β - decay, isotopes lose the same amount of energy. Consequently, based on the law of conservation of energy, W. Pauli predicted that another light particle called an antineutrino would be ejected. An antineutrino has no charge or mass. Energy losses by β-particles when passing through matter are caused mainly by ionization processes. Part of the energy is lost to X-ray radiation when β-particles are decelerated by the nuclei of the absorbing substance. Since β - particles have low mass, a single charge and very high velocities, their ionizing ability is low (100 times less than that of α - particles), therefore, the penetrating ability (range) of β - particles is significantly greater than for α-particles.
R β air =200 m, R β Pb ≈ 3 mm
β - - decay occurs in natural and artificial radioactive nuclei. β + - only with artificial radioactivity.
Bias rule for β - - decay:
c) K - capture (electronic capture) - the nucleus absorbs one of the electrons located on the K shell (less oftenLor M) of its atom, as a result of which one of the protons turns into a neutron, emitting a neutrino
Scheme K - capture:
The space in the electron shell vacated by the captured electron is filled with electrons from the overlying layers, resulting in the formation of X-rays.
- γ-rays.
Typically, all types of radioactivity are accompanied by the emission of γ-rays. γ-rays are electromagnetic radiation with wavelengths from one to hundredths of an angstrom λ’=~ 1-0.01 Å=10 -10 -10 -12 m. The energy of γ-rays reaches millions of eV.
W γ ~ MeB
1eV=1.6·10 -19 J
A nucleus undergoing radioactive decay, as a rule, turns out to be excited, and its transition to the ground state is accompanied by the emission of a γ photon. In this case, the energy of the γ-photon is determined by the condition
where E 2 and E 1 are the energy of the nucleus.
E 2 - energy in the excited state;
E 1 - energy in the ground state.
The absorption of γ-rays by matter is due to three main processes:
- photoelectric effect (with hv < l MэB);
- the formation of electron-positron pairs;
or
- scattering (Compton effect) -
Absorption of γ-rays occurs according to Bouguer’s law:
where μ- linear coefficient attenuation, depending on the energies of γ - rays and the properties of the medium;
І 0 - intensity of the incident parallel beam;
Iis the intensity of the beam after passing through the thickness of the substance X cm.
γ-rays are one of the most penetrating radiations. For the hardest rays (hν max) the thickness of the half-absorption layer is 1.6 cm in lead, 2.4 cm in iron, 12 cm in aluminum, and 15 cm in earth.
§2 The basic law of radioactive decay.
Number of decayed nucleidN proportional to the initial number of cores N and decay timedt, dN~ N dt. The basic law of radioactive decay in differential form:
The coefficient λ is called the decay constant for a given type of nuclei. The “-“ sign means thatdNmust be negative, since the final number of undecayed nuclei is less than the initial one.
therefore, λ characterizes the fraction of nuclei that decay per unit time, i.e., it determines the rate of radioactive decay. λ does not depend on external conditions, but is determined only by the internal properties of the nuclei. [λ]=с -1 .
The basic law of radioactive decay in integral form
Where N 0 - the initial number of radioactive nuclei att=0;
N- the number of undecayed nuclei at a timet;
λ is the radioactive decay constant.
In practice, the rate of decay is judged using not λ, but T 1/2 - half-life - the time during which half of the original number of nuclei decays. Relationship between T 1/2 and λ
T 1/2 U 238 = 4.5 10 6 years, T 1/2 Ra = 1590 years, T 1/2 Rn = 3.825 days. Number of decays per unit time A = -dN/ dtis called the activity of a given radioactive substance.
From
should
[A] = 1Becquerel = 1decay/1s;
[A] = 1Ci = 1Curie = 3.7 10 10 Bq.
Law of Activity Change
where A 0 = λ N 0 - initial activity at a point in timet= 0;
A - activity at a timet.
Many years ago, people wondered what all substances were made of. The first who tried to answer it was the ancient Greek scientist Democritus, who believed that all substances consist of molecules. It is now known that molecules are built from atoms. Atoms are made up of even smaller particles. At the center of the atom is the nucleus, which contains protons and neutrons. The smallest particles - electrons - move in orbits around the nucleus. Their mass is negligible compared to the mass of the nucleus. But only calculations and knowledge of chemistry will help you find the mass of the nucleus. To do this, you need to determine the number of protons and neutrons in the nucleus. Look at the table values of the masses of one proton and one neutron and find their total mass. This will be the mass of the nucleus.
You can often come across the question of how to find the mass, knowing the speed. According to the classical laws of mechanics, mass does not depend on the speed of the body. After all, if a car starts to pick up speed as it starts moving, this does not mean at all that its mass will increase. However, at the beginning of the twentieth century, Einstein presented a theory according to which this dependence exists. This effect is called relativistic increase in body weight. And it manifests itself when the speeds of bodies approach the speed of light. Modern charged particle accelerators make it possible to accelerate protons and neutrons to such high speeds. And in fact, in this case, an increase in their masses was recorded.
But we still live in a world of high technology, but low speeds. Therefore, in order to know how to calculate the mass of matter, you do not need to accelerate the body to the speed of light and learn Einstein’s theory. Body weight can be measured on a scale. True, not every body can be put on the scale. Therefore, there is another way to calculate mass from its density.
The air around us, the air that is so necessary for humanity, also has its own mass. And when solving the problem of how to determine the mass of air, for example, in a room, it is not necessary to count the number of air molecules and sum up the mass of their nuclei. You can simply determine the volume of the room and multiply it by the air density (1.9 kg/m3).
Scientists have now learned to calculate with great accuracy the masses of different bodies, from atomic nuclei to the mass of the globe and even stars located at a distance of several hundred light years from us. Mass as physical quantity, is a measure of the inertia of a body. More massive bodies are said to be more inert, that is, they change their speed more slowly. Therefore, after all, speed and mass turn out to be interconnected. But the main feature of this quantity is that any body or substance has mass. There is no matter in the world that does not have mass!
Core charge
The nucleus of any atom is positively charged. The carrier of positive charge is the proton. Since the charge of a proton is numerically equal to the charge of an electron $e$, we can write that the charge of the nucleus is equal to $+Ze$ ($Z$ is an integer that indicates the serial number of a chemical element in D. I. Mendeleev’s periodic system of chemical elements). The number $Z$ also determines the number of protons in the nucleus and the number of electrons in the atom. Therefore it is called the atomic number of the nucleus. Electric charge is one of the main characteristics of the atomic nucleus, on which the optical, chemical and other properties of atoms depend.
Core mass
Another important characteristic of the nucleus is its mass. The mass of atoms and nuclei is usually expressed in atomic mass units (amu). It is customary to consider $1/12$ of the mass of a carbon nuclide $^(12)_6C$ as an atomic mass unit:
where $N_A=6.022\cdot 10^(23)\ mol^-1$ is Avogadro's number.
According to Einstein's relation $E=mc^2$, the mass of atoms is also expressed in energy units. Because the:
- proton mass $m_p=1.00728\ amu=938.28\ MeV$,
- neutron mass $m_n=1.00866\ amu=939.57\ MeV$,
- electron mass $m_e=5.49\cdot 10^(-4)\ amu=0.511\ MeV$,
As you can see, the mass of the electron is negligibly small in comparison with the mass of the nucleus, then the mass of the nucleus almost coincides with the mass of the atom.
Mass is different from whole numbers. Nuclear mass, expressed in amu. and rounded to a whole number is called the mass number, denoted by the letter $A$ and determines the number of nucleons in the nucleus. The number of neutrons in the nucleus is $N=A-Z$.
To designate nuclei, the symbol $^A_ZX$ is used, where $X$ means the chemical symbol of a given element. Atomic nuclei with the same number of protons but different mass numbers are called isotopes. In some elements, the number of stable and unstable isotopes reaches tens, for example, uranium has $14$ isotopes: from $^(227)_(92)U\ $ to $^(240)_(92)U$.
Most chemical elements existing in nature are a mixture of several isotopes. It is the presence of isotopes that explains the fact that some natural elements have masses that differ from whole numbers. For example, natural chlorine consists of $75\%$ $^(35)_(17)Cl$ and $24\%$ $^(37)_(17)Cl$, and its atomic mass is $35.5$ a.u. .m. in most atoms, except hydrogen, the isotopes have almost the same physical and Chemical properties. But behind their exclusively nuclear properties, isotopes differ significantly. Some of them can be stable, others - radioactive.
Nuclei with the same mass numbers, but different $Z$ values are called isobars, for example, $^(40)_(18)Ar$, $^(40)_(20)Ca$. Nuclei with the same number of neutrons are called isotones. Among light nuclei there are so-called “mirror” pairs of nuclei. These are pairs of nuclei in which the numbers $Z$ and $A-Z$ are swapped. Examples of such nuclei could be $^(13)_6C\ $ and $^(13_7)N$ or $^3_1H$ and $^3_2He$.
Atomic nucleus size
Assuming the atomic nucleus to be approximately spherical, we can introduce the concept of its radius $R$. Note that in some nuclei there is a slight deviation from symmetry in the distribution of electric charge. In addition, atomic nuclei are not static, but dynamic systems, and the concept of the radius of a nucleus cannot be represented as the radius of a ball. For this reason, the size of the nucleus must be taken as the area in which nuclear forces manifest themselves.
When creating the quantitative theory of scattering of $\alpha $ - particles, E. Rutherford proceeded from the assumptions that the atomic nucleus and $\alpha $ - particle interact according to Coulomb's law, i.e. that the electric field around the nucleus has spherical symmetry. The scattering of an $\alpha $ particle occurs in full accordance with Rutherford's formula:
This occurs for $\alpha $ - particles whose energy $E$ is quite small. In this case, the particle is not able to overcome the Coulomb potential barrier and subsequently does not reach the region of action of nuclear forces. As the particle energy increases to a certain boundary value $E_(gr)$ $\alpha $ -- the particle reaches this boundary. Then in the scattering of $\alpha $ - particles there is a deviation from the Rutherford formula. From the relation
Experiments show that the radius $R$ of the nucleus depends on the number of nucleons that enter the nucleus. This dependence can be expressed by the empirical formula:
where $R_0$ is a constant, $A$ is a mass number.
The sizes of nuclei are determined experimentally by the scattering of protons, fast neutrons or high-energy electrons. There are a number of other indirect methods for determining the size of nuclei. They are based on the connection between the lifetime of $\alpha $ -- radioactive nuclei and the energy of $\alpha $ -- particles released by them; on the optical properties of so-called mesoatoms, in which one electron is temporarily captured by a muon; by comparing the binding energy of a pair of mirror atoms. These methods confirm the empirical dependence $R=R_0A^(1/3)$, and using these measurements the value of the constant $R_0=\left(1.2-1.5\right)\cdot 10^(-15) was established \ m$.
Note also that the unit of distance in atomic physics and particle physics is taken as the “Fermi” unit of measurement, which is equal to $(10)^(-15)\ m$ (1 f=$(10)^(-15)\ m )$.
The radii of atomic nuclei depend on their mass number and are in the range from $2\cdot 10^(-15)\ m\ to\\ 10^(-14)\ m$. if we express $R_0$ from the formula $R=R_0A^(1/3)$ and write it in the form $\left(\frac(4\pi R^3)(3A)\right)=const$, then we can see that each nucleon contains approximately the same volume. This means that the density of nuclear matter is approximately the same for all nuclei. Based on the existing data on the sizes of atomic nuclei, we find the average value of the density of nuclear matter:
As we can see, the density of nuclear matter is very high. This is due to the action of nuclear forces.
Energy of communication. Nuclear mass defect
When comparing the sum of the rest masses of the nucleons that form the nucleus with the mass of the nucleus, it was noticed that for all chemical elements the following inequality is true:
where $m_p$ is the mass of the proton, $m_n$ is the mass of the neutron, $m_я$ is the mass of the nucleus. The value $\triangle m$, which expresses the mass difference between the mass of nucleons that form the nucleus and the mass of the nucleus, is called the nuclear mass defect
Important information about the properties of the nucleus can be obtained without delving into the details of the interaction between the nucleons of the nucleus, based on the law of conservation of energy and the law of proportionality of mass and energy. Depending on how much as a result of any change in mass $\triangle m$ there is a corresponding change in energy $\triangle E$ ($\triangle E=\triangle mc^2$), then during the formation of a nucleus a certain amount of energy is released. According to the law of conservation of energy, the same amount of energy is needed to divide the nucleus into its constituent particles, i.e. move nucleons one from another at the same distances at which there is no interaction between them. This energy is called the binding energy of the nucleus.
If the nucleus has $Z$ protons and mass number $A$, then the binding energy is equal to:
Note 1
Note that this formula is not entirely convenient to use, because The tables do not list the masses of nuclei, but the masses that determine the masses of neutral atoms. Therefore, for the convenience of calculations, the formula is transformed in such a way that it includes the masses of atoms, not nuclei. For this purpose, on the right side of the formula we add and subtract the mass $Z$ of electrons $(m_e)$. Then
\c^2==\leftc^2.\]
$m_(()^1_1H)$ is the mass of the hydrogen atom, $m_a$ is the mass of the atom.
In nuclear physics, energy is often expressed in megaelectron volts (MeV). If we're talking about about the practical application of nuclear energy, it is measured in joules. In the case of comparing the energy of two nuclei, the mass unit of energy is used - the ratio between mass and energy ($E=mc^2$). A mass unit of energy ($le$) equals energy, which corresponds to a mass of one amu. It is equal to $931,502$ MeV.
Picture 1.
In addition to energy, the specific binding energy is important - the binding energy that falls on one nucleon: $w=E_(st)/A$. This value changes relatively slowly compared to the change in the mass number $A$, having an almost constant value of $8.6$ MeV in the middle part periodic table and decreases to its edges.
As an example, let us calculate the mass defect, binding energy and specific binding energy of the nucleus of a helium atom.
Mass defect
Binding energy in MeV: $E_(bv)=\triangle m\cdot 931.502=0.030359\cdot 931.502=28.3\ MeV$;
Specific binding energy: $w=\frac(E_(st))(A)=\frac(28.3\ MeV)(4\approx 7.1\ MeV).$
How to find the mass of the nucleus of an atom? and got the best answer
Answer from NiNa Martushova[guru]
A = number p + number n. That is, the entire mass of the atom is concentrated in the nucleus, since the electron has a negligible mass, equal to 11800 a. e.m., while the proton and neutron each have a mass of 1 atomic mass unit. Relative atomic mass is a fractional number because it is the arithmetic mean of the atomic masses of all isotopes of a given chemical element, taking into account their abundance in nature.
Answer from Yoehmet[guru]
Take the mass of the atom and subtract the mass of all the electrons.
Answer from Vladimir Sokolov[guru]
Sum up the mass of all the protons and neutrons in the nucleus. You will get a lot of money.
Answer from Dashka[newbie]
periodic table to help
Answer from Anastasia Durakova[active]
Find the value of the relative mass of an atom in the periodic table, round it to the nearest whole number - this will be the mass of the atomic nucleus. Nuclear mass, or mass number of an atom, is made up of the number of protons and neutrons in the nucleus
A = number p + number n. That is, the entire mass of the atom is concentrated in the nucleus, since the electron has a negligible mass, equal to 11800 a. e.m., while the proton and neutron each have a mass of 1 atomic mass unit. Relative atomic mass is a fractional number because it is the arithmetic mean of the atomic masses of all isotopes of a given chemical element, taking into account their abundance in nature. periodic table to help
Answer from 3 answers[guru]
Hello! Here is a selection of topics with answers to your question: How to find the mass of the nucleus of an atom?
