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 AU. e. m., while the proton and neutron each have a mass of 1 atomic mass unit. The 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 prevalence 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 the mass of all the protons and neutrons in the nucleus. You'll get a lot in em.

Answer from Dasha[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 up to a whole number - this will be the mass of the atom's nucleus. The mass of the nucleus, or the 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 AU. e. m., while the proton and neutron each have a mass of 1 atomic mass unit. The 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 prevalence 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?

atomic nucleus is the central part of the atom, made up of protons and neutrons (collectively called nucleons).

The nucleus was discovered by E. Rutherford in 1911 while studying the passage α -particles through matter. It turned out that almost the entire mass of an atom (99.95%) is concentrated in the nucleus. The size of the atomic nucleus is of the order of 10 -1 3 -10 - 12 cm, which is 10,000 times smaller than the size of the electron shell.

The planetary model of the atom proposed by E. Rutherford and his experimental observation of hydrogen nuclei knocked out α -particles from the nuclei of other elements (1919-1920), led the scientist to the idea of proton. The term proton was introduced in the early 20s of the XX century.

Proton (from Greek. protons- first, character p) is a stable elementary particle, the nucleus of a hydrogen atom.

Proton- a positively charged particle, the charge of which is equal in absolute value to the charge of an electron e\u003d 1.6 10 -1 9 Cl. The mass of a proton is 1836 times the mass of an electron. Rest mass of a proton m p= 1.6726231 10 -27 kg = 1.007276470 amu

The second particle in the nucleus is neutron.

Neutron (from lat. neuter- neither one nor the other, a symbol n) is an elementary particle that has no charge, i.e., neutral.

The mass of the neutron is 1839 times the mass of the electron. The mass of a neutron is almost equal to (slightly larger than) that of a proton: the rest mass of a free neutron m n= 1.6749286 10 -27 kg = 1.0008664902 amu and exceeds the proton mass by 2.5 electron masses. Neutron, along with the proton under the common name nucleon is part of the atomic nucleus.

The neutron was discovered in 1932 by D. Chadwig, a student of E. Rutherford, during the bombardment of beryllium α -particles. The resulting radiation with high penetrating power (it overcame an obstacle made of a lead plate 10–20 cm thick) intensified its effect when passing through the paraffin plate (see figure). The estimation of the energy of these particles from the tracks in the cloud chamber made by the Joliot-Curies and additional observations made it possible to exclude the initial assumption that this γ -quanta. The great penetrating power of new particles, called neutrons, was explained by their electrical neutrality. After all, charged particles actively interact with matter and quickly lose their energy. The existence of neutrons was predicted by E. Rutherford 10 years before the experiments of D. Chadwig. On hit α -particles in the nuclei of beryllium, the following reaction occurs:

Here is the symbol of the neutron; its charge is equal to zero, and the relative atomic mass is approximately equal to one. A neutron is an unstable particle: a free neutron in a time of ~ 15 min. decays into a proton, an electron and a neutrino - a particle devoid of rest mass.

After the discovery of the neutron by J. Chadwick in 1932, D. Ivanenko and W. Heisenberg independently proposed proton-neutron (nucleon) model of the nucleus. According to this model, the nucleus consists of protons and neutrons. Number of protons Z coincides with the serial number of the element in the table of D. I. Mendeleev.

Core charge Q determined by the number of protons Z, which are part of the nucleus, and is a multiple of the absolute value of the electron charge e:

Q = + Ze.

Number Z called nuclear charge number or atomic number.

Mass number of the nucleus BUT called the total number of nucleons, i.e., protons and neutrons contained in it. The number of neutrons in a nucleus is denoted by the letter N. So the mass number is:

A = Z + N.

The nucleons (proton and neutron) are assigned a mass number equal to one, and the electron is assigned a zero value.

The idea of ​​the composition of the nucleus was also facilitated by the discovery isotopes.

Isotopes (from the Greek. isos equal, same and topoa- place) - these are varieties of atoms of the same chemical element, the atomic nuclei of which have the same number of protons ( Z) and a different number of neutrons ( N).

The nuclei of such atoms are also called isotopes. Isotopes are nuclides one element. Nuclide (from lat. nucleus- nucleus) - any atomic nucleus (respectively, an atom) with given numbers Z and N. The general designation of nuclides is ……. where X- symbol of a chemical element, A=Z+N- mass number.

Isotopes occupy the same place in the Periodic Table of the Elements, hence their name. As a rule, isotopes differ significantly in their nuclear properties (for example, in their ability to enter into nuclear reactions). The chemical (and almost equally physical) properties of isotopes are the same. This is explained by the fact that the chemical properties of an element are determined by the charge of the nucleus, since it is this charge that affects the structure of the electron shell of the atom.

The exception is isotopes of light elements. Isotopes of hydrogen 1 H — protium, 2 H— deuterium, 3 H — tritium they differ so much in mass that their physical and chemical properties are different. Deuterium is stable (i.e., not radioactive) and is included as a small impurity (1: 4500) in ordinary hydrogen. Deuterium combines with oxygen to form heavy water. It boils at normal atmospheric pressure at 101.2°C and freezes at +3.8°C. Tritium β is radioactive with a half-life of about 12 years.

All chemical elements have isotopes. Some elements have only unstable (radioactive) isotopes. For all elements, radioactive isotopes have been artificially obtained.

Isotopes of uranium. The element uranium has two isotopes - with mass numbers 235 and 238. The isotope is only 1/140 of the more common.

§1 Charge and mass, 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. A carrier of a 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 over energy shells and subshells essentially depends on their total number in the atom. Therefore, the charge of the nucleus largely determines the distribution of electrons over their states in the atom and the position of the element in the periodic system of Mendeleev. The nuclear charge isqI = z· e, where z- the charge number of the nucleus, equal to the ordinal number of the element in the Mendeleev 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 for hydrogen, is approximately 2.5 10 -4 masses of atoms. The mass of atoms is expressed in atomic mass units (a.m.u.). For a.u.m. accepted 1/12 mass of carbon atom.

1 amu \u003d 1.6605655 (86) 10 -27 kg.

mI = m a -Z me.

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 the mass number m and denoted by the letter BUT. Designation of a chemical element: BUT- mass number, X - symbol of a chemical element,Z-charging number - serial number in the periodic table ():

Beryllium; Isotopes: , ", .

Core Radius:

where A is the mass number.

§2 Composition of the core

The nucleus of a hydrogen atomcalled proton

mproton= 1.00783 amu , .

Hydrogen atom diagram

In 1932, a particle called the neutron was discovered, which has a mass close to that of a proton (mneutron= 1.00867 a.m.u.) and does not have an 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 BUT. 3 ordinal numberZdetermines the number of protons in the nucleus, the number of neutronsN \u003d A - Z.

Elementary particles - protons and neutrons entering into the core, are collectively known as nucleons. 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 state with a charge+ e, and neutron with a charge of 0.

§3 Binding energy of the nucleus. mass defect. nuclear forces

Nuclear particles - protons and neutrons - are firmly held inside the nucleus, so very large attractive forces act between them, capable of withstanding the huge repulsive forces between like-charged protons. These special forces arising at small distances between nucleons are called nuclear forces. Nuclear forces are not electrostatic (Coulomb).

The study of the nucleus showed that the nuclear forces acting between nucleons have the following features:

a) these are short-range forces - manifested 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 - charge independence of nuclear forces. The nuclear forces acting between a neutron and a proton, between two neutrons, between two protons are equal. Proton and neutron in relation to nuclear forces are the same.

The binding energy is a measure of the stability of an atomic nucleus. The binding energy of the nucleus is equal to the work that must be done to split the nucleus into its constituent nucleons without imparting kinetic energy to them

M I< Σ( m p + m n)

Me - the mass of the nucleus

Measurement of the masses of nuclei shows that the rest mass of the nucleus is less than the sum of the rest masses of its constituent nucleons.

Value

serves as a measure of the binding energy and is called the mass defect.

Einstein's equation in special relativity relates the energy and rest mass of a particle.

In the general case, the binding energy of the nucleus can be calculated by the formula

where Z - charge number (number of protons in the nucleus);

BUT- 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) are equal to 1 a.u. m. (a.m.u. - atomic mass unit) corresponds to the binding energy (E St) equal to 1 a.u.e. (a.u.e. - atomic unit of energy) and equal to 1a.u.m. s 2 = 931 MeV.

§ 4 Nuclear reactions

Changes in nuclei during their interaction with individual particles and with each other are usually called nuclear reactions.

There are the following, the most common nuclear reactions.

1. 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.

1. Radiative capture reaction . The incident particle gets stuck in the nucleus, but the excited nucleus emits excess energy, emitting a γ-photon (used in the operation of nuclear reactors)

An example of a neutron capture reaction by cadmium

or phosphorus

1. Scattering. The intermediate nucleus emits a particle identical to

with the flown one, and it can be:

Elastic scattering neutrons with carbon (used in reactors to moderate neutrons):

Inelastic scattering :

1. fission reaction. This is a reaction that always proceeds with the release of energy. It is the basis for the technical production and use of nuclear energy. During the fission reaction, the excitation of the intermediate compound nucleus is so great that it is divided into two, approximately equal fragments, with the release of several neutrons.

If the excitation energy is low, then the separation 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 introduced by the neutron is large, then the excited nucleus begins to deform, a constriction is formed in it and as a result it is divided into two fragments that fly apart at tremendous speeds, while two neutrons are emitted
(Fig. 2).

Chain reaction- self-developing fission reaction. To implement it, it is necessary that of the secondary neutrons produced during one fission event, at least one can cause the next fission event: (since some neutrons can participate in capture reactions without causing fission). Quantitatively, the condition for the existence of a chain reaction expresses multiplication factor

k < 1 - цепная реакция невозможна, k = 1 (m = m kr ) - chain reactions with a constant number of neutrons (in a nuclear reactor),k > 1 (m > m kr ) are nuclear bombs.

RADIOACTIVITY

§1 Natural radioactivity

Radioactivity is the spontaneous transformation of unstable nuclei of one element into nuclei of another element. natural radioactivity called the radioactivity observed in the unstable isotopes that exist in nature. Artificial radioactivity is called the radioactivity of isotopes obtained as a result of nuclear reactions.

Types of radioactivity:

1. α-decay.

Emission by the nuclei of some chemical elements of the α-system of two protons and two neutrons connected together (a-particle - the nucleus of a helium atom)

α-decay is inherent in heavy nuclei with BUT> 200 andZ > 82. When moving in a substance, α-particles produce strong ionization of atoms on their way (ionization is the separation of electrons from an atom), acting on them with their electric field. The distance over which an α-particle flies in matter until it stops completely is called particle range or penetrating power(denotedR, [ R ] = m, cm). . Under normal conditions, an α-particle forms in air 30,000 pairs of ions per 1 cm path. Specific ionization is the number of pairs of ions formed per 1 cm of the path length. The α-particle has a strong biological effect.

Shift rule for alpha decay:

2. β-decay.

a) electronic (β -): the nucleus emits an electron and an electron antineutrino

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

These processes occur by converting one type of nucleon into 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 charge (+e = 1.6 10 -19 C)

It follows from the experiment that during β - decay, isotopes lose the same amount of energy. Therefore, on the basis of the law of conservation of energy, W. Pauli predicted that another light particle, called antineutrino, is ejected. An antineutrino has no charge or mass. Losses of energy by β-particles during their passage through matter are caused mainly by ionization processes. Part of the energy is lost to X-rays during deceleration of β-particles by the nuclei of the absorbing substance. Since β-particles have a small mass, a unit charge and very high speeds, their ionizing ability is small (100 times less than that of α-particles), therefore, the penetrating power (mileage) of β-particles is significantly greater than α-particles.

Rβ air =200 m, Rβ Pb ≈ 3 mm

β - - decay occurs in natural and artificial radioactive nuclei. β + - only with artificial radioactivity.

Displacement rule for β - - decay:

c) K - capture (electronic capture) - the nucleus absorbs one of the electrons located on the shell K (less oftenLor M) of its atom, as a result of which one of the protons turns into a neutron, while 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 X-rays.

• γ-rays.

Usually, all types of radioactivity are accompanied by the emission of γ-rays. γ-rays are electromagnetic radiation having 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 ~ MeV

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 is 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 is a linear attenuation coefficient, depending on the energies of γ rays and the properties of the medium;

І 0 is the intensity of the incident parallel beam;

Iis the intensity of the beam after passing through a substance of thickness X cm.

γ-rays are one of the most penetrating radiations. For the hardest rays (hvmax) 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 Basic law of radioactive decay.

Number of decayed nucleidN proportional to the original 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 decaying per unit time, i.e., 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]=s -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 non-decayed nuclei at a timet;

λ is the radioactive decay constant.

The decay rate in practice is judged using not λ, but T 1/2 - the half-life - the time during which half of the original number of nuclei decays. Relationship 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 The number of decays per unit time A \u003d -dN/ dtis called the activity of a given radioactive substance.

From

follows,

[A] \u003d 1 Becquerel \u003d 1 disintegration / 1 s;

[A] \u003d 1Ci \u003d 1Curie \u003d 3.7 10 10 Bq.

Law of activity change

where A 0 = λ N 0 - initial activity at timet= 0;

A - activity at a timet.

Many years ago, people wondered what all substances are made of. The first who tried to answer it was the ancient Greek scientist Democritus, who believed that all substances are composed of molecules. We now know that molecules are built from atoms. Atoms are made up of even smaller particles. At the center of an 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 how to find the mass of the nucleus, only calculations and knowledge of chemistry will help. To do this, you need to determine the number of protons and neutrons in the nucleus. View the tabular values ​​of the masses of one proton and one neutron and find their total mass. This will be the mass of the nucleus.

Often you can come across such a question, how to find the mass, knowing the speed. According to the classical laws of mechanics, the mass does not depend on the speed of the body. After all, if a car, moving away, begins to pick up its speed, 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 the relativistic increase in body mass. And it manifests itself when the speeds of bodies approach the speed of light. Modern 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 a substance, it is not at all necessary 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 scales. Therefore, there is another way to calculate mass from its density.

The air around us, the air that is so necessary for mankind, 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 with great accuracy to calculate the masses of different bodies, from the nuclei of atoms to the mass of the globe and even stars located at a distance of several hundred light years from us. Mass, as a physical quantity, is a measure of the inertia of a body. More massive bodies, they say, are more inert, that is, they change their speed more slowly. Therefore, after all, speed and mass are 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!

Investigating the passage of an α-particle through a thin gold foil (see Section 6.2), E. Rutherford came to the conclusion that an atom consists of a heavy positively charged nucleus and electrons surrounding it.

core called the center of the atom,in which almost all the mass of an atom and its positive charge is concentrated.

AT composition of the atomic nucleus includes elementary particles : protons and neutrons (nucleons from the Latin word nucleus- nucleus). Such a proton-neutron model of the nucleus was proposed by the Soviet physicist in 1932 D.D. Ivanenko. The proton has a positive charge e + = 1.06 10 -19 C and a rest mass m p\u003d 1.673 10 -27 kg \u003d 1836 me. Neutron ( n) is a neutral particle with rest mass m n= 1.675 10 -27 kg = 1839 me(where the mass of the electron me, is equal to 0.91 10 -31 kg). On fig. 9.1 shows the structure of the helium atom according to the ideas of the late XX - early XXI century.

Core charge equals Ze, where e is the charge of the proton, Z- charge number equal to serial number chemical element in Mendeleev's periodic system of elements, i.e. the number of protons in the nucleus. The number of neutrons in a nucleus is denoted N. Usually Z > N.

Nuclei with Z= 1 to Z = 107 – 118.

Number of nucleons in the nucleus A = Z + N called mass number . nuclei with the same Z, but different BUT called isotopes. Kernels, which, at the same A have different Z, are called isobars.

The nucleus is denoted by the same symbol as the neutral atom, where X is the symbol for a chemical element. For example: hydrogen Z= 1 has three isotopes: – protium ( Z = 1, N= 0), is deuterium ( Z = 1, N= 1), – tritium ( Z = 1, N= 2), tin has 10 isotopes, and so on. The vast majority of isotopes of the same chemical element have the same chemical and close physical properties. In total, about 300 stable isotopes and more than 2000 natural and artificially obtained are known. radioactive isotopes.

The size of the nucleus is characterized by the radius of the nucleus, which has a conditional meaning due to the blurring of the border of the nucleus. Even E. Rutherford, analyzing his experiments, showed that the size of the nucleus is approximately 10–15 m (the size of an atom is 10–10 m). There is an empirical formula for calculating the core radius:

where R 0 = (1.3 - 1.7) 10 -15 m. From this it can be seen that the volume of the nucleus is proportional to the number of nucleons.

The density of the nuclear substance is on the order of 10 17 kg/m 3 and is constant for all nuclei. It greatly exceeds the density of the densest ordinary substances.

Protons and neutrons are fermions, because have spin ħ /2.

The nucleus of an atom has own angular momentum – nuclear spin :

,

(9.1.2)

where I – internal(complete)spin quantum number.

Number I accepts integer or half-integer values ​​0, 1/2, 1, 3/2, 2, etc. Kernels with even BUT have integer spin(in units ħ ) and obey the statistics Bose–Einstein(bosons). Kernels with odd BUT have half-integer spin(in units ħ ) and obey the statistics Fermi–Dirac(those. nuclei are fermions).

Nuclear particles have their own magnetic moments, which determine the magnetic moment of the nucleus as a whole. The unit for measuring the magnetic moments of nuclei is nuclear magneton μ poison:

Here e is the absolute value of the electron charge, m p is the mass of the proton.

Nuclear magneton in m p/me= 1836.5 times smaller than the Bohr magneton, hence it follows that the magnetic properties of atoms are determined by the magnetic properties of its electrons .

There is a relationship between the spin of the nucleus and its magnetic moment:

where γ poison - nuclear gyromagnetic ratio.

The neutron has a negative magnetic moment μ n≈ – 1.913μ poison because the direction of the neutron spin and its magnetic moment are opposite. The magnetic moment of the proton is positive and equal to μ R≈ 2.793μ poison. Its direction coincides with the direction of the proton spin.

The distribution of the electric charge of protons over the nucleus is generally asymmetric. The measure of deviation of this distribution from spherically symmetric is quadrupole electric moment of the nucleus Q. If the charge density is assumed to be the same everywhere, then Q determined only by the shape of the nucleus. So, for an ellipsoid of revolution

,

(9.1.5)

where b is the semiaxis of the ellipsoid along the spin direction, a- axis in the perpendicular direction. For a nucleus stretched along the direction of the spin, b > a and Q> 0. For a nucleus oblate in this direction, b < a and Q < 0. Для сферического распределения заряда в ядре b = a and Q= 0. This is true for nuclei with spin equal to 0 or ħ /2.

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