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Nick Connor

What is Isotope – Nuclide – Definition

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Isotopes are nuclides that have the same atomic number and are therefore the same element, but differ in the number of neutrons. The stable isotopes (plus a few of the unstable isotopes) are the atoms that are found in the naturally occurring elements in nature. Material Properties

Isotope

Proton Number - Atomic NumberIn nuclear physics and nuclear chemistry, the various species of atoms whose nuclei contain particular numbers of protons and neutrons are called nuclides. Nuclides are also characterized by its nuclear energy states (e.g. metastable nuclide 242mAm). Each nuclide is denoted by chemical symbol of the element (this specifies Z) with the atomic mass number as superscript. Isotopes are nuclides that have the same atomic number and are therefore the same element, but differ in the number of neutrons. Hydrogen (H), for example , consist of one electron and one proton. The number of neutrons in a nucleus is known as the neutron number and is given the symbol N. The total number of nucleons, that is, protons and neutrons in a nucleus, is equal to Z + N = A, where A is called the atomic mass number.

Thus the symbol 1H refers to the nuclide of hydrogen with a single proton as nucleus. 2H is the hydrogen nuclide with a neutron as well as a proton in the nucleus (2H is also called deuterium or heavy hydrogen). Atoms such as 1H, 2H whose nuclei contain the same number of protons but different number of neutrons (different A) are isotopes. Uranium, for instance, has three isotopes occurring in nature – 238U, 235U and 234U. All have 92 protons in their nuclei. But, whereas the 235U isotope has 143 neutrons in its nucleus, that of the 238U isotope contains 146 neutrons. The stable isotopes (plus a few of the unstable isotopes) are the atoms that are found in the naturally occurring elements in nature. However, they are not found in equal amounts. Some isotopes of a given element are more abundant than others. For example 99,27% of naturally occuring uranium atoms are the isotope 238U, 0,72% are the isotope 235U and 0,0055% are the isotope 234U.

Because all the isotopes of a given element exhibit the same chemical properties, their separation is very difficult by chemical means. The traditional methods of isotope separation are based directly on the atomic weight of the isotope or based on the small differences in chemical reaction rates produced by different atomic weights. These methods have included mass spectometry, centrifugal separation and processes that depend on the different rates at which heavy and light particles diffuse.

Nuclide chart - Nuclear Stability
Segre chart – This chart shows a plot of the known nuclides as a function of their atomic and neutron numbers. It can be observed from the chart that there are more neutrons than protons in nuclides with Z greater than about 20 (Calcium). These extra neutrons are necessary for stability of the heavier nuclei. The excess neutrons act somewhat like nuclear glue.

Isotopes of the highest importance in reactor physics

Uranium

Uranium is a naturally-occurring chemical element with atomic number 92 which means there are 92 protons and 92 electrons in the atomic structure. The chemical symbol for uranium is U. Uranium is commonly found  at low levels (a few ppm – parts per million) in all rocks, soil, water, plants, and animals (including humans). Uranium occurs also in seawater, and can be recovered from the ocean water. Significant concentrations of uranium occur in some substances such as uraninite (the most common uranium ore), phosphate rock deposits, and other minerals.

Natural uranium consists primarily of isotope 238U (99.28%), therefore the atomic mass of uranium element is close to the atomic mass of 238U isotope (238.03u).  Natural uranium also consists of two other isotopes: 235U (0.71%) and 234U (0.0054%). The abundance of  isotopes in the nature is caused by difference in the half-lifes. All three naturally-occurring isotopes of uranium (238U, 235U and 234U)  are unstable. On the other hand these isotopes (except 234U) belong to primordial nuclides, because their half-life is comparable to the age of the Earth (~4.5×109 years for 238U).

In nuclear reactors we have to consider three artificial isotopes, 236U, 233U and 232U. These are produced by transmutation in nuclear reactors from 235U and 232Th.

Xenon

Xenon is a naturally-occurring chemical element with atomic number 54 which means there are 54 protons and 54 electrons in the atomic structure. The chemical symbol for xenon is Xe. Xenon is a colorless, dense, odorless noble gas found in the Earth’s atmosphere in trace amounts.

Natural xenon consists of eight stable isotopes, 124Xe (0.095%), 126Xe (0.089%), 128Xe (1.91%), 129Xe (26.4%), 130Xe (4.07%), 131Xe (21.23%), 132Xe (26.91%),  134Xe (10.44%), and one isotope with very long half-life 136Xe (8.86%).

In nuclear industry, especially artificial xenon 135 has a tremendous impact on the operation of a nuclear reactor. For physicists and for reactor operators, it is important to understand the mechanisms that produce and remove xenon from the reactor to predict how the reactor will respond following changes in power level.

Another important isotope is the xenon 133, which has half-life of 5.2 days, and its presence in a reactor coolant indicates (together with xenon 135) a possible failure of fuel cladding. A new defect will often result in a step increase in only the Xe-133 activity, which is measured from reactor coolant. As the defect enlarges, the release rate of the soluble, longer-lived nuclides, particularly I-131, I-134, Cs-134, and Cs-137 will increase.

Boron

Boron is a naturally-occurring chemical element with atomic number 5 which means there are 5 protons and 5 electrons in the atomic structure. The chemical symbol for boron is B.

Natural boron consists primarily of two stable isotopes, 11B (80.1%) and  10B (19.9%). In nuclear industry boron is commonly used as a neutron absorberdue to the high neutron cross-section of isotope  10B. Its (n,alpha) reaction cross-section for thermal neutrons is about 3840 barns (for 0.025 eV neutron). Isotope  11B has absorption cross-section for thermal neutrons about 0.005 barns (for 0.025 eV neutron). Most of (n,alpha) reactions of thermal neutrons are 10B(n,alpha)7Li reactions accompanied by 0.48 MeV gamma emission.

(n,alpha) reactions of 10B

Moreover, isotope 10B has high (n,alpha) reaction cross-section along the entire neutron energy spectrum. The cross-sections of most other elements becomes very small at high energies as in the case of cadmium. The cross-section of 10B decreases monotonically with energy. For fast neutrons its cross-section is on the order of barns.

References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See also:

Nuclide

We hope, this article, Isotope – Nuclide, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about materials and their properties.

What is Nuclide – Definition

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In nuclear physics and nuclear chemistry, the various species of atoms whose nuclei contain particular numbers of protons and neutrons are called nuclides. Nuclides are also characterized by its nuclear energy states (e.g. metastable nuclide 242mAm). Material Properties

Nuclides

Proton Number - Atomic NumberIn nuclear physics and nuclear chemistry, the various species of atoms whose nuclei contain particular numbers of protons and neutrons are called nuclides. Nuclides are also characterized by its nuclear energy states (e.g. metastable nuclide 242mAm). Each nuclide is denoted by chemical symbol of the element (this specifies Z) with the atomic mass number as superscript. Hydrogen (H), for example , consist of one electron and one proton. The number of neutrons in a nucleus is known as the neutron number and is given the symbol N. The total number of nucleons, that is, protons and neutrons in a nucleus, is equal to Z + N = A, where A is called the atomic mass number.

Thus the symbol 1H refers to the nuclide of hydrogen with a single proton as nucleus. 2H is the hydrogen nuclide with a neutron as well as a proton in the nucleus (2H is also called deuterium or heavy hydrogen). Atoms such as 1H, 2H whose nuclei contain the same number of protons but different number of neutrons (different A) are known as isotopes. Uranium, for instance, has three isotopes occurring in nature – 238U, 235U and 234U. All have 92 protons in their nuclei. But, whereas the 235U isotope has 143 neutrons in its nucleus, that of the 238U isotope contains 146 neutrons. The stable isotopes (plus a few of the unstable isotopes) are the atoms that are found in the naturally occurring elements in nature. However, they are not found in equal amounts. Some isotopes of a given element are more abundant than others. For example 99,27% of naturally occuring uranium atoms are the isotope 238U, 0,72% are the isotope 235U and 0,0055% are the isotope 234U. As can be seen, all nuclides can be grouped according to number of protons, neutrons and its nuclear energy states:

  • Isotopes. Isotopes are nuclides that have the same atomic number and are therefore the same element, but differ in the number of neutrons.
  • Isotones. Isotones are nuclides that have the same neutron number and are therefore different elements, since they must differ in the number of protons.
  • Isobars. Isobars are nuclides that have the same mass number and are therefore different elements, since they must differ in the number of protons.
  • Isomers. Isomers are nuclides with equal proton number and equal mass number (thus making them by definition the same isotope), but different energy states.
Nuclide chart - Nuclear Stability
Segre chart – This chart shows a plot of the known nuclides as a function of their atomic and neutron numbers. It can be observed from the chart that there are more neutrons than protons in nuclides with Z greater than about 20 (Calcium). These extra neutrons are necessary for stability of the heavier nuclei. The excess neutrons act somewhat like nuclear glue.

Examples of Nuclides

Uranium

Uranium is a naturally-occurring chemical element with atomic number 92 which means there are 92 protons and 92 electrons in the atomic structure. The chemical symbol for uranium is U. Uranium is commonly found  at low levels (a few ppm – parts per million) in all rocks, soil, water, plants, and animals (including humans). Uranium occurs also in seawater, and can be recovered from the ocean water. Significant concentrations of uranium occur in some substances such as uraninite (the most common uranium ore), phosphate rock deposits, and other minerals.

Natural uranium consists primarily of isotope 238U (99.28%), therefore the atomic mass of uranium element is close to the atomic mass of 238U isotope (238.03u).  Natural uranium also consists of two other isotopes: 235U (0.71%) and 234U (0.0054%). The abundance of  isotopes in the nature is caused by difference in the half-lifes. All three naturally-occurring isotopes of uranium (238U, 235U and 234U)  are unstable. On the other hand these isotopes (except 234U) belong to primordial nuclides, because their half-life is comparable to the age of the Earth (~4.5×109 years for 238U).

In nuclear reactors we have to consider three artificial isotopes, 236U, 233U and 232U. These are produced by transmutation in nuclear reactors from 235U and 232Th.

Xenon

Xenon is a naturally-occurring chemical element with atomic number 54 which means there are 54 protons and 54 electrons in the atomic structure. The chemical symbol for xenon is Xe. Xenon is a colorless, dense, odorless noble gas found in the Earth’s atmosphere in trace amounts.

Natural xenon consists of eight stable isotopes, 124Xe (0.095%), 126Xe (0.089%), 128Xe (1.91%), 129Xe (26.4%), 130Xe (4.07%), 131Xe (21.23%), 132Xe (26.91%),  134Xe (10.44%), and one isotope with very long half-life 136Xe (8.86%).

In nuclear industry, especially artificial xenon 135 has a tremendous impact on the operation of a nuclear reactor. For physicists and for reactor operators, it is important to understand the mechanisms that produce and remove xenon from the reactor to predict how the reactor will respond following changes in power level.

Another important isotope is the xenon 133, which has half-life of 5.2 days, and its presence in a reactor coolant indicates (together with xenon 135) a possible failure of fuel cladding. A new defect will often result in a step increase in only the Xe-133 activity, which is measured from reactor coolant. As the defect enlarges, the release rate of the soluble, longer-lived nuclides, particularly I-131, I-134, Cs-134, and Cs-137 will increase.

Boron

Boron is a naturally-occurring chemical element with atomic number 5 which means there are 5 protons and 5 electrons in the atomic structure. The chemical symbol for boron is B.

Natural boron consists primarily of two stable isotopes, 11B (80.1%) and  10B (19.9%). In nuclear industry boron is commonly used as a neutron absorberdue to the high neutron cross-section of isotope  10B. Its (n,alpha) reaction cross-section for thermal neutrons is about 3840 barns (for 0.025 eV neutron). Isotope  11B has absorption cross-section for thermal neutrons about 0.005 barns (for 0.025 eV neutron). Most of (n,alpha) reactions of thermal neutrons are 10B(n,alpha)7Li reactions accompanied by 0.48 MeV gamma emission.

(n,alpha) reactions of 10B

Moreover, isotope 10B has high (n,alpha) reaction cross-section along the entire neutron energy spectrum. The cross-sections of most other elements becomes very small at high energies as in the case of cadmium. The cross-section of 10B decreases monotonically with energy. For fast neutrons its cross-section is on the order of barns.

References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See also:

Atom

We hope, this article, Nuclide, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about materials and their properties.

What is Nucleon – Structure of Atomic Nucleus – Definition

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The particles that comprise atomic nuclei are termed nucleons. A nucleon is either a proton or a neutron. Neutrons and protons, i.e. nucleons, are bound together in the atomic nucleus, where they account for 99.9 percent of the atom’s mass. Material Properties

Nucleons

Nuclear Force - Principle
The residual strong force acts indirectly through the virtual π and ρ mesons, which transmit the force between nucleons that holds the nucleus together.

In physics, the atomic nucleus is the central part of an atom. In comparison to an atom, it is much more smaller and contains most of the mass of the atom. Atomic nuclei are not elementary particles, they are themselves composed of more fundamental particles. The particles that comprise atomic nuclei are termed nucleons. A nucleon is either a proton or a neutron. Neutrons and protons, i.e. nucleons, are bound together in the atomic nucleus, where they account for 99.9 percent of the atom’s mass. Research in high-energy particle physics in the 20th century revealed that neither the neutron nor the proton is not the smallest building block of matter.

See also: What is Proton

See also: What is Neutron

Protons and neutrons have also their structure. Inside the protons and neutrons, we find true elementary particles called quarks. The proton and neutron are both baryons and both fermions. The proton carries a positive net charge and the neutron carries a zero net charge. Thus, they can be viewed as two states of the same nucleon. In order to distinguish between these nucleons, modern understanding defines isospin as a quantum number related to the strong force. The observations have showed that the strong interaction does not distinguish between these nucleon. The strength of the strong interaction between any pair of nucleons is the same, independent of whether they are interacting as neutrons or as protons. Instead of regarding protons and neutrons as totally different species, as far as strong interactions are concerned, they are regarded as being different isospin states of the same underlying nucleon particle.

The proton has isotopic spin ½ as the neutron has isotopic spin ½, but in case of proton the spin is pointing upwards and the spin of neutron is pointing downwards.

Within the nucleus, protons and neutrons are bound together through the residual strong force, a fundamental interaction that governs the behaviour of the quarks that make up the individual protons and neutrons. The residual strong force, also known as the nuclear force, acts to hold neutrons and protons together in nuclei. In nuclei, this force acts against the enormous repulsive electromagnetic force of the protons. The term residual is associated with the fact, it is the residuum of the fundamental strong interaction between the quarks that make up the protons and neutrons. The strong interaction is very complicated interaction, because it significantly varies with distance. At distances comparable to the diameter of a proton, the strong force is approximately 100 times as strong as electromagnetic force. At smaller distances, however, the strong force between quarks becomes weaker, and the quarks begin to behave like independent particles. In particle physics, this effect is known as asymptotic freedom.

Nucleon Number

Proton Number - Atomic NumberThe total number of protons and neutrons in the nucleus of an atom is called the atomic mass number (also called nucleon number) of the atom and is given the symbol A. Neutron number plus atomic number equals nucleon number: N+Z=A. The difference between the neutron number and the atomic number is known as the neutron excess: D = N – Z = A – 2Z.

Atomic mass number (nucleon number) determines especially the atomic mass of atoms. The nucleon number is different for each different isotope of a chemical element. The nucleon number is written either after the element name or as a superscript to the left of an element’s symbol. For example, the most common isotope of carbon is carbon-12, or 12C. Note that, the unit of measure for mass is the atomic mass unit (amu). One atomic mass unit is equal to 1.66 x 10-24 grams.

Besides the thermodynamics/thermodynamic-properties/what-is-mass-and-weight/standard-kilogram/”>standard kilogram, it is a second mass standard. It is the carbon-12 atom, which, by international agreement, has been assigned a mass of 12 atomic mass units (u). The relation between the two units is one atomic mass unit is equal:

1u = 1.66 x 10-24 grams.

One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1 g/mol.

For 12C the atomic mass is exactly 12u, since the atomic mass unit is defined from it. For other isotopes, the isotopic mass usually differs and is usually within 0.1 u of the mass number. For example, 63Cu (29 protons and 34 neutrons) has a mass number of 63 and an isotopic mass in its nuclear ground state is 62.91367 u.

There are two reasons for the difference between mass number and isotopic mass, known as the mass defect:

  1. The neutron is slightly heavier than the proton. This increases the mass of nuclei with more neutrons than protons relative to the atomic mass unit scale based on 12C with equal numbers of protons and neutrons.
  2. The nuclear binding energy varies between nuclei. A nucleus with greater binding energy has a lower total energy, and therefore a lower mass according to Einstein’s mass-energy equivalence relation E = mc2. For 63Cu the atomic mass is less than 63 so this must be the dominant factor.

Note that, it was found the rest mass of an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, neutrons and electrons. Mass was no longer considered unchangeable in the closed system. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (E=mc2), this binding energy is proportional to this mass difference and it is known as the mass defect.

Conservation of Nucleon Number in Nuclear Reactions

In general, the nucleon number is not conserved in nuclear reactions.

In analyzing nuclear reactions, we apply the many conservation laws. Nuclear reactions are subject to classical conservation laws for charge, momentum, angular momentum, and energy (including rest energies).  Additional conservation laws, not anticipated by classical physics, are are electric charge, lepton number and baryon number. Certain of these laws are obeyed under all circumstances, others are not. We have accepted conservation of energy and momentum. In reactor physics (non-relativistic physics), we assume that the number of protons (the atomic number), the number of neutrons (the neutron number) and its sum (the nucleon number) are usually separately conserved. We shall find circumstances and conditions in which  this rule is not true. Where we are considering non-relativistic nuclear reactions, it is essentially true. However, where we are considering relativistic nuclear energies or those involving the weak interactions (e.g. in beta decay the atomic number is not conserved), we shall find that these principles must be extended.

Conservation of Baryon Number

Instead of nucleon number conservation, physicists define the baryon number, which is a conserved quantum number in all particle reactions.

Baryon number is a generalization of nucleon number, which is conserved in nonrelativistic nuclear reactions and decays. The law of conservation of baryon numberstates that:

The sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction.

Number of Nucleons and Nuclear Stability

Nuclide chart - Nuclear Stability
Segre chart – This chart shows a plot of the known nuclides as a function of their atomic and neutron numbers. It can be observed from the chart that there are more neutrons than protons in nuclides with Z greater than about 20 (Calcium). These extra neutrons are necessary for stability of the heavier nuclei. The excess neutrons act somewhat like nuclear glue.

Nuclear stability is a concept that helps to identify the stability of an isotope. To identify the stability of an isotope it is needed to find the ratio of neutrons to protons. To determine the stability of an isotope you can use the ratio neutron/proton (N/Z). Also to help understand this concept there is a chart of the nuclides, known as a Segre chart. This chart shows a plot of the known nuclides as a function of their atomic and neutron numbers. It can be observed from the chart that there are more neutrons than protons in nuclides with Z greater than about 20 (Calcium). These extra neutrons are necessary for stability of the heavier nuclei. The excess neutrons act somewhat like nuclear glue.

See also: Livechart – iaea.org

Detail of Nuclide Chart.

Detail of Nuclide Chart.
Source: Livechart – IAEA.org

Atomic nuclei consist of protons and neutrons, which attract each other through the nuclear force, while protons repel each other via the electric force due to their positive charge. These two forces compete, leading to various stability of nuclei. There are only certain combinations of neutrons and protons, which forms stable nuclei.

Neutrons stabilize the nucleus, because they attract each other and protons , which helps offset the electrical repulsion between protons. As a result, as the number of protons increases, an increasing ratio of neutrons to protons is needed to form a stable nucleus. If there are too many or too few neutrons for a given number of protons, the resulting nucleus is not stable and it undergoes radioactive decay. Unstable isotopes decay through various radioactive decay pathways, most commonly alpha decay, beta decay, or electron capture. Many other rare types of decay, such as spontaneous fission or neutron emission are known. It should be noted that all of these decay pathways may be accompanied by the subsequent emission of gamma radiation. Pure alpha or beta decays are very rare.

See also: Pauli Exclusion Principle

See also: Unstable Nuclei

Magic Numbers of Nucleons

A magic number is a number of nucleons in a nucleus, which corresponds to complete shells within the atomic nucleus. Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy per nucleon than one would expect based upon predictions such as the mass formula of von Weizsaecker (also called the semi-empirical mass formula – SEMF) and are hence more stable against nuclear decay. Magic numbers are predicted by the nuclear shell model and are proved by observations that have shown that there are sudden discontinuities in the proton and neutron separation energies at specific values of Z and N. These correspond to the closing of shells (or sub-shells). Nuclei with closed shells are more tightly bound than the next higher number. The closing of shells occurs at Z or N = 2, 8, 20, 28, (40), 50, 82, 126. It is found that nuclei with even numbers of protons and neutrons are more stable than those with odd numbers. Nuclei which have both neutron number and proton number equal to one of the magic numbers can be called “doubly magic“, and are found to be particularly stable.magic numbers - doubly magic nucleiThere are further special propertis of nuclei, which have a magic number of nucleons:

  1. Higher abundance in nature. For example, helium-4 is among the most abundant (and stable) nuclei in the universe.
  2. The stable elements at the end of the decay series all have a “magic number” of neutrons or protons. The nuclei He-4, O-16, and Pb-208 (82 protons and 126 neutrons) that contain magic numbers of both neutrons and protons are particularly stable. The relative stability of these nuclei is reminiscent of that of inert gas atoms (closed electron shells).
  3. Nuclei with N = magic number have much lower neutron absorption cross-sections than surrounding isotopes.
  4. These nuclei appear to be perfectly spherical in shape; they have zero quadrupole electric moments.
  5. Magic number nuclei have higher first excitation energy.
References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See also:

Atomic Nucleus

We hope, this article, Nucleon – Structure of Atomic Nucleus, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about materials and their properties.

What is Neutron Star as “Giant Nucleus” – Definition

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A neutron star is the collapsed core of a large star (usually of a red giant). Neutron stars are the smallest and densest stars known to exist and they are rotating extremely rapidly. Since they have some similar properties as atomic nuclei, neutron stars are sometimes described as giant nuclei. Material Properties

Neutron Star as “Giant Nucleus”

A neutron star is the collapsed core of a large star (usually of a red giant). Neutron stars are the smallest and densest stars known to exist and they are rotating extremely rapidly. A neutron star is basically a giant atomic nucleus about 11 km in diameter made especially of neutrons. It is believed that under the immense pressures of a collapsing massive stars going supernova it is possible for the electrons and protons  to combine to form neutrons via electron capture, releasing a huge amount of neutrinos. Since they have some similar properties as atomic nuclei, neutron stars are sometimes described as giant nuclei. But be careful, neutron stars and atomic nuclei are held together by different forces.  A nucleus is held together by the strong force, while a neutron star is held together by gravitational force.

On the other hand, neutron stars are partially supported against further collapse by neutron degeneracy (via degeneracy pressure), a phenomenon described by the Pauli exclusion principle. In general, in a highly dense state of matter, where gravitational pressure is extreme, quantum mechanical effects are significant. Degenerate matter is usually modelled as an ideal Fermi gas, in which the Pauli exclusion principle prevents identical fermions from occupying the same quantum state. Similarly, white dwarfs are supported against collapse by electron degeneracy pressure, which is analogous to neutron degeneracy.

References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See also:

Atomic Nucleus

We hope, this article, Neutron Star as “Giant Nucleus”, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about materials and their properties.

What is Magic Number of Protons and Neutrons – Definition

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A magic number is a number of nucleons in a nucleus, which corresponds to complete shells within the atomic nucleus. Nuclei which have both neutron number and proton number equal to one of the magic numbers can be called “doubly magic”, and are found to be particularly stable.

Magic Numbers of Protons and Neutrons

A magic number is a number of nucleons in a nucleus, which corresponds to complete shells within the atomic nucleus. Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy per nucleon than one would expect based upon predictions such as the mass formula of von Weizsaecker (also called the semi-empirical mass formula – SEMF) and are hence more stable against nuclear decay. Magic numbers are predicted by the nuclear shell model and are proved by observations that have shown that there are sudden discontinuities in the proton and neutron separation energies at specific values of Z and N. These correspond to the closing of shells (or sub-shells). Nuclei with closed shells are more tightly bound than the next higher number. The closing of shells occurs at Z or N = 2, 8, 20, 28, (40), 50, 82, 126. It is found that nuclei with even numbers of protons and neutrons are more stable than those with odd numbers. Nuclei which have both neutron number and proton number equal to one of the magic numbers can be called “doubly magic“, and are found to be particularly stable.magic numbers - doubly magic nucleiThere are further special propertis of nuclei, which have a magic number of nucleons:

  1. Higher abundance in nature. For example, helium-4 is among the most abundant (and stable) nuclei in the universe.
  2. The stable elements at the end of the decay series all have a “magic number” of neutrons or protons. The nuclei He-4, O-16, and Pb-208 (82 protons and 126 neutrons) that contain magic numbers of both neutrons and protons are particularly stable. The relative stability of these nuclei is reminiscent of that of inert gas atoms (closed electron shells).
  3. Nuclei with N = magic number have much lower neutron absorption cross-sections than surrounding isotopes.
  4. These nuclei appear to be perfectly spherical in shape; they have zero quadrupole electric moments.
  5. Magic number nuclei have higher first excitation energy.
References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See also:

Atomic Nucleus

We hope, this article, Magic Number of Protons and Neutrons, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about materials and their properties.

What is Nuclear Shell Model – Shell Model of Nucleus – Definition

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In nuclear physics, the nuclear shell model is a theoretical model to describe the atomic nucleus. It must be noted this model is based on the Pauli exclusion principle. The nuclear shell model is partly analogous to the atomic shell model which describes the arrangement of electrons in an atom

Nuclear Shell Model

Shell model of nucleusIn nuclear physics, the nuclear shell model is a theoretical model to describe the atomic nucleus. The nuclear shell model was proposed by Dmitry Ivanenko in 1932 and further developed independently by several physicists such as Maria Goeppert-Mayer, Eugene Paul Wigner and J. Hans D. Jensen in 1949. It must be noted this model is based on the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels.

The nuclear shell model is partly analogous to the atomic shell model which describes the arrangement of electrons in an atom, in that a filled shell results in greater stability. Nucleons are added to shells which increase with energy that orbit around a central potential. In the atomic shell model the central potential around which the electrons orbit is generated by the nucleus. Nucleons are added to shells which increase with energy that orbit around a central potential.

In comparison to atomic shell model, the atomic nucleus governed by two different forces. The residual strong force, also known as the nuclear force, acts to hold neutrons and protons together in nuclei. In nuclei, this force acts against the enormous repulsive electromagnetic force of the protons. The term residual is associated with the fact, it is the residuum of the fundamental strong interaction between the quarks that make up the protons and neutrons. The strong interaction is very complicated interaction, because it significantly varies with distance. At distances comparable to the diameter of a proton, the strong force is approximately 100 times as strong as electromagnetic force. At smaller distances, however, the strong force between quarks becomes weaker, and the quarks begin to behave like independent particles. In particle physics, this effect is known as asymptotic freedom.

With the enormous strong force acting between individual nucleons and with so many nucleons to collide with, how can nucleons orbit a central potential without interacting? This problem is explained by the Pauli exclusion principle, which states that two fermions cannot occupy the same quantum state. In other words, the interaction will not occur, if the higher energy shells are fully occupied and the energy imparted to the nucleon during the collision is insufficient to promote the nucleon to an unfilled orbit. As a result, the nucleons orbit independent of one another.

The nuclear shell model was able to describe many phenomena like the magic numbers, the ground state spin and parity etc..

Magic Numbers of Protons and Neutrons

A magic number is a number of nucleons in a nucleus, which corresponds to complete shells within the atomic nucleus. Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy per nucleon than one would expect based upon predictions such as the mass formula of von Weizsaecker (also called the semi-empirical mass formula – SEMF) and are hence more stable against nuclear decay. Magic numbers are predicted by the nuclear shell model and are proved by observations that have shown that there are sudden discontinuities in the proton and neutron separation energies at specific values of Z and N. These correspond to the closing of shells (or sub-shells). Nuclei with closed shells are more tightly bound than the next higher number. The closing of shells occurs at Z or N = 2, 8, 20, 28, (40), 50, 82, 126. It is found that nuclei with even numbers of protons and neutrons are more stable than those with odd numbers. Nuclei which have both neutron number and proton number equal to one of the magic numbers can be called “doubly magic“, and are found to be particularly stable.magic numbers - doubly magic nucleiThere are further special propertis of nuclei, which have a magic number of nucleons:

  1. Higher abundance in nature. For example, helium-4 is among the most abundant (and stable) nuclei in the universe.
  2. The stable elements at the end of the decay series all have a “magic number” of neutrons or protons. The nuclei He-4, O-16, and Pb-208 (82 protons and 126 neutrons) that contain magic numbers of both neutrons and protons are particularly stable. The relative stability of these nuclei is reminiscent of that of inert gas atoms (closed electron shells).
  3. Nuclei with N = magic number have much lower neutron absorption cross-sections than surrounding isotopes.
  4. These nuclei appear to be perfectly spherical in shape; they have zero quadrupole electric moments.
  5. Magic number nuclei have higher first excitation energy.

Neutron Star as “Giant Nucleus”

A neutron star is the collapsed core of a large star (usually of a red giant). Neutron stars are the smallest and densest stars known to exist and they are rotating extremely rapidly. A neutron star is basically a giant atomic nucleus about 11 km in diameter made especially of neutrons. It is believed that under the immense pressures of a collapsing massive stars going supernova it is possible for the electrons and protons  to combine to form neutrons via electron capture, releasing a huge amount of neutrinos. Since they have some similar properties as atomic nuclei, neutron stars are sometimes described as giant nuclei. But be careful, neutron stars and atomic nuclei are held together by different forces.  A nucleus is held together by the strong force, while a neutron star is held together by gravitational force.

On the other hand, neutron stars are partially supported against further collapse by neutron degeneracy (via degeneracy pressure), a phenomenon described by the Pauli exclusion principle. In general, in a highly dense state of matter, where gravitational pressure is extreme, quantum mechanical effects are significant. Degenerate matter is usually modelled as an ideal Fermi gas, in which the Pauli exclusion principle prevents identical fermions from occupying the same quantum state. Similarly, white dwarfs are supported against collapse by electron degeneracy pressure, which is analogous to neutron degeneracy.

References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See also:

Atomic Nucleus

We hope, this article, Nuclear Shell Model – Shell Model of Nucleus, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about materials and their properties.

What is Radius and Density of Atomic Nucleus – Definition

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Radius and Density of Atomic Nucleus. Nuclear density is the density of the nucleus of an atom. It is the ratio of mass per unit volume inside the nucleus. Since atomic nucleus carries most of atom’s mass and atomic nucleus is very small in comparison to entire atom, the nuclear density is very high. Material Properties

Radius and Density of Atomic Nucleus

A figurative depiction of the helium-4 atom with the electron cloud in shades of gray. Protons and neutrons are most likely found in exactly the same space, at the central point. Source wikipedia.org License CC BY-SA 3.0

Typical nuclear radii are of the order 10−14 m. Assuming spherical shape, nuclear radii can be calculated according to following formula:

r = r0 . A1/3

where r0 = 1.2 x 10-15 m = 1.2 fm

If we use this approximation, we therefore expect the geometrical cross-sections of nuclei to be of the order of πr2 or 4.5×10−30 m² for hydrogen nuclei or 1.74×10−28 m² for 238U nuclei.

Nuclear density is the density of the nucleus of an atom. It is the ratio of mass per unit volume inside the nucleus. Since atomic nucleus carries most of atom’s mass and atomic nucleus is very small in comparison to entire atom, the nuclear density is very high.

The nuclear density for a typical nucleus can be approximately calculated from the size of the nucleus and from its mass. For example, natural uranium consists primarily of isotope 238U (99.28%), therefore the atomic mass of uranium element is close to the atomic mass of 238U isotope (238.03u). Its radius of this nucleus will be:

r = r0 . A1/3 = 7.44 fm.

Assuming it is spherical, its volume will be:

V = 4πr3/3 = 1.73 x 10-42 m3.

The usual definition of nuclear density gives for its density:

ρnucleus = m / V = 238 x 1.66 x 10-27 / (1.73 x 10-42) = 2.3 x 1017kg/m3.

Thus, the density of nuclear material is more than 2.1014 times greater than that of water. It is an immense density. The descriptive term nuclear density is also applied to situations where similarly high densities occur, such as within neutron stars. Such immense densities are also found in neutron stars.

References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See also:

Atom

We hope, this article, Radius and Density of Atomic Nucleus, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about materials and their properties.

What is Mass of Nucleus – Atomic Mass Unit – Definition

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The mass of the nucleus is associated with the atomic mass number. The unit of measure for mass is the atomic mass unit (amu). One atomic mass unit is equal to 1.66 x 10-24 grams. Material Properties

Mass of Nucleus – Atomic Mass Unit

Proton Number - Atomic NumberAs was written, almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. The mass of the nucleus is associated with the atomic mass number, which is the total number of protons and neutrons in the nucleus of an atom. The mass number is different for each different isotope of a chemical element. The mass number is written either after the element name or as a superscript to the left of an element’s symbol. For example, the most common isotope of carbon is carbon-12, or 12C.

The size and mass of atoms are so small that the use of normal measuring units, while possible, is often inconvenient. Units of measure have been defined for mass and energy on the atomic scale to make measurements more convenient to express. The unit of measure for mass is the atomic mass unit (amu). One atomic mass unit is equal to 1.66 x 10-24 grams.

Besides the thermodynamics/thermodynamic-properties/what-is-mass-and-weight/standard-kilogram/”>standard kilogram, it is a second mass standard. It is the carbon-12 atom, which, by international agreement, has been assigned a mass of 12 atomic mass units (u). The relation between the two units is one atomic mass unit is equal:

1u = 1.66 x 10-24 grams.

One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1 g/mol.

For 12C the atomic mass is exactly 12u, since the atomic mass unit is defined from it. For other isotopes, the isotopic mass usually differs and is usually within 0.1 u of the mass number. For example, 63Cu (29 protons and 34 neutrons) has a mass number of 63 and an isotopic mass in its nuclear ground state is 62.91367 u.

There are two reasons for the difference between mass number and isotopic mass, known as the mass defect:

  1. The neutron is slightly heavier than the proton. This increases the mass of nuclei with more neutrons than protons relative to the atomic mass unit scale based on 12C with equal numbers of protons and neutrons.
  2. The nuclear binding energy varies between nuclei. A nucleus with greater binding energy has a lower total energy, and therefore a lower mass according to Einstein’s mass-energy equivalence relation E = mc2. For 63Cu the atomic mass is less than 63 so this must be the dominant factor.

Note that, it was found the rest mass of an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, neutrons and electrons. Mass was no longer considered unchangeable in the closed system. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (E=mc2), this binding energy is proportional to this mass difference and it is known as the mass defect.

nuclear fission vs fusion

References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See also:

Atom

We hope, this article, Mass of Nucleus – Atomic Mass Unit, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about materials and their properties.

What is Atomic Nucleus – Definition

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The atomic nucleus is the central part of an atom. The atomic nucleus also contains all of its positive electric charge (in protons), while all of its negative charge is distributed in the electron cloud. The atomic nucleus was discovered by Ernest Rutherford, who proposed a new model of the atom. Material Properties

Atomic Nucleus

A figurative depiction of the helium-4 atom with the electron cloud in shades of gray. Protons and neutrons are most likely found in exactly the same space, at the central point. Source wikipedia.org License CC BY-SA 3.0

In physics, the atomic nucleus is the central part of an atom. In comparison to an atom, it is much more smaller and contains most of the mass of the atom. The atomic nucleus also contains all of its positive electric charge (in protons), while all of its negative charge is distributed in the electron cloud.

The atomic nucleus was discovered by Ernest Rutherford, who proposed a new model of the atom based on Geiger-Marsden experiments. These experiments were performed between 1908 and 1913 by Hans Geiger and Ernest Marsden under the direction of Ernest Rutherford. These experiments were a landmark series of experiments by which scientists discovered that every atom contains a nucleus (whose diameter is of the order 10-14m) where all of its positive charge and most of its mass are concentrated in a small region called an atomic nucleus. In Rutherford’s atom, the diameter of its sphere (about 10-10 m) of influence is determined by its electrons. In other words, the nucleus occupies only about 10-12 of the total volume of the atom or less (the nuclear atom is largely empty space), but it contains all the positive charge and at least 99.95% of the total mass of the atom.

After discovery of the neutron in 1932 by the English physicist James Chadwick, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg.

All matter except dark matter is made of molecules, which are themselves made of atoms. The atoms consist of two parts. An atomic nucleus and an electron cloud, which are bound together by electrostatic force. The nucleus itself is generally made of protons and neutrons but even these are composite objects. Inside the protons and neutrons, we find the quarks.

Inside the atomic nucleus, the residual strong force, also known as the nuclear force, acts to hold neutrons and protons together in nuclei. In nuclei, this force acts against the enormous repulsive electromagnetic force of the protons. The term residual is associated with the fact, it is the residuum of the fundamental strong interaction between the quarks that make up the protons and neutrons. The residual strong force acts indirectly through the virtual π and ρ mesons, which transmit the force between nucleons that holds the nucleus together.

Properties of Nucleus

The nuclear properties (atomic mass, nuclear cross-sections) of the element are determined by the number of protons (atomic number) and number of neutrons (neutron number). For example, actinides with odd neutron number are usually fissile (fissionable with slow neutrons) while actinides with even neutron number are usually not fissile (but are fissionable with fast neutrons). Heavy nuclei with an even number of protons and an even number of neutrons are (due to Pauli exclusion principle) very stable thanks to the occurrence of ‘paired spin’. On the other hand, nuclei with an odd number of protons and neutrons are mostly unstable.

Mass of Nucleus

Proton Number - Atomic NumberAs was written, almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. The mass of the nucleus is associated with the atomic mass number, which is the total number of protons and neutrons in the nucleus of an atom. The mass number is different for each different isotope of a chemical element. The mass number is written either after the element name or as a superscript to the left of an element’s symbol. For example, the most common isotope of carbon is carbon-12, or 12C.

The size and mass of atoms are so small that the use of normal measuring units, while possible, is often inconvenient. Units of measure have been defined for mass and energy on the atomic scale to make measurements more convenient to express. The unit of measure for mass is the atomic mass unit (amu). One atomic mass unit is equal to 1.66 x 10-24 grams.

Besides the thermodynamics/thermodynamic-properties/what-is-mass-and-weight/standard-kilogram/”>standard kilogram, it is a second mass standard. It is the carbon-12 atom, which, by international agreement, has been assigned a mass of 12 atomic mass units (u). The relation between the two units is one atomic mass unit is equal:

1u = 1.66 x 10-24 grams.

One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1 g/mol.

For 12C the atomic mass is exactly 12u, since the atomic mass unit is defined from it. For other isotopes, the isotopic mass usually differs and is usually within 0.1 u of the mass number. For example, 63Cu (29 protons and 34 neutrons) has a mass number of 63 and an isotopic mass in its nuclear ground state is 62.91367 u.

There are two reasons for the difference between mass number and isotopic mass, known as the mass defect:

  1. The neutron is slightly heavier than the proton. This increases the mass of nuclei with more neutrons than protons relative to the atomic mass unit scale based on 12C with equal numbers of protons and neutrons.
  2. The nuclear binding energy varies between nuclei. A nucleus with greater binding energy has a lower total energy, and therefore a lower mass according to Einstein’s mass-energy equivalence relation E = mc2. For 63Cu the atomic mass is less than 63 so this must be the dominant factor.

Note that, it was found the rest mass of an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, neutrons and electrons. Mass was no longer considered unchangeable in the closed system. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (E=mc2), this binding energy is proportional to this mass difference and it is known as the mass defect.

Radius and Density of Atomic Nucleus

Typical nuclear radii are of the order 10−14 m. Assuming spherical shape, nuclear radii can be calculated according to following formula:

r = r0 . A1/3

where r0 = 1.2 x 10-15 m = 1.2 fm

If we use this approximation, we therefore expect the geometrical cross-sections of nuclei to be of the order of πr2 or 4.5×10−30 m² for hydrogen nuclei or 1.74×10−28 m² for 238U nuclei.

Nuclear density is the density of the nucleus of an atom. It is the ratio of mass per unit volume inside the nucleus. Since atomic nucleus carries most of atom’s mass and atomic nucleus is very small in comparison to entire atom, the nuclear density is very high.

The nuclear density for a typical nucleus can be approximately calculated from the size of the nucleus and from its mass. For example, natural uranium consists primarily of isotope 238U (99.28%), therefore the atomic mass of uranium element is close to the atomic mass of 238U isotope (238.03u). Its radius of this nucleus will be:

r = r0 . A1/3 = 7.44 fm.

Assuming it is spherical, its volume will be:

V = 4πr3/3 = 1.73 x 10-42 m3.

The usual definition of nuclear density gives for its density:

ρnucleus = m / V = 238 x 1.66 x 10-27 / (1.73 x 10-42) = 2.3 x 1017kg/m3.

Thus, the density of nuclear material is more than 2.1014 times greater than that of water. It is an immense density. The descriptive term nuclear density is also applied to situations where similarly high densities occur, such as within neutron stars. Such immense densities are also found in neutron stars.

Excited Nucleus – Nuclear Resonance

Compound state - resonance
Energy levels of compound state. For neutron absorption reaction on 238U the first resonance E1 corresponds to the excitation energy of 6.67eV. E0 is a base state of 239U.

Highly excited nuclei formed by the combination of the incident particle and target nucleus are known as nuclear resonances. If a target nucleus X is bombarded with particles a, it is sometimes observed that the ensuing nuclear reaction takes place with appreciable probability only if the energy of the particle a is in the neighborhood of certain definite energy values. These energy values are referred to as resonance energies. The compound nuclei of these certain energies are referred to as nuclear resonances. Resonances are usually found only at relatively low energies of the projectile. The widths of the resonances increase in general with increasing energies. At higher energies the widths may reach the order of the distances between resonances and then no resonances can be observed.

References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See also:

Atom

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What is Pauli Exclusion Principle – Definition

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The Pauli exclusion principle is the principle, formulated by Wolfgang Pauli in 1925. It is the Pauli exclusion principle that requires the electrons in an atom to occupy different energy levels instead of them all condensing in the ground state. Material Properties

Pauli Exclusion Principle

The Pauli exclusion principle is the principle, formulated by Wolfgang Pauli in 1925, which states that:

No two electrons can occupy the same quantum-mechanical state within a given quantum system simultaneously.

In terms of the quantum numbers:

No two electrons in an atom can have the same values of all four quantum numbers.

It is impossible for two electrons of a multielectron atom to have the same values of the four quantum numbers:

  • n – the principal quantum number,
  • ℓ –  the angular momentum quantum number
  • mℓ – the magnetic quantum number,
  • ms – the spin quantum number.

Mathematically this means the wavefunctions of the two particles must be antisymmetric which leads to the the probability amplitude of the wavefunction going to zero if the two fermionic particles are the same.

Pauli Exclusion PrincipleIt is the Pauli exclusion principle that requires the electrons in an atom to occupy different energy levels instead of them all condensing in the ground state. The ordering of the electrons in the ground state of multielectron atoms, starts with the lowest energy state (ground state) and moves progressively from there up the energy scale until each of the atom’s electrons has been assigned a unique set of quantum numbers. This fact has key implications for the building up of the periodic table of elements.

It must be noted, chemical properties of atoms are determined by the number of protons, in fact, by number and arrangement of electrons. The configuration of these electrons follows from the principles of quantum mechanics as well as the Pauli exclusion principle. The number of electrons in each element’s electron shells, particularly the outermost valence shell, is the primary factor in determining its chemical bonding behavior. As such, without the Pauli exclusion principle, there would be no chemistry.

This principle must be considered for any particles whose spin quantum number s is not zero or an integer. Therefore, this principle applies not only to electrons but also to protons and neutrons, all of which have half-integer spin.

Pauli Exclusion Principle and Nuclear Stability

Nuclide chart - Nuclear Stability
Segre chart – This chart shows a plot of the known nuclides as a function of their atomic and neutron numbers. It can be observed from the chart that there are more neutrons than protons in nuclides with Z greater than about 20 (Calcium). These extra neutrons are necessary for stability of the heavier nuclei. The excess neutrons act somewhat like nuclear glue.

Atomic nuclei consist of protons and neutrons, which attract each other through the nuclear force, while protons repel each other via the electromagnetic force due to their positive charge. These two forces compete, leading to various stability of nuclei. There are only certain combinations of neutrons and protons, which forms stable nuclei. Neutrons stabilize the nucleus, because they attract each other and protons , which helps offset the electrical repulsion between protons. As a result, as the number of protons increases, an increasing ratio of neutrons to protons is needed to form a stable nucleus. If there are too many (neutrons also obey the Pauli exclusion principle) or too few neutrons for a given number of protons, the resulting nucleus is not stable and it undergoes radioactive decay. Unstable isotopes decay through various radioactive decay pathways, most commonly alpha decay, beta decay, or electron capture. Many other rare types of decay, such as spontaneous fission or neutron emission are known.

The Pauli exclusion principle also influences the critical energy of fissile and fissionable nuclei. For example, actinides with odd neutron number are usually fissile (fissionable with slow neutrons) while actinides with even neutron number are usually not fissile (but are fissionable with fast neutrons). Heavy nuclei with an even number of protons and an even number of neutrons are (due to Pauli exclusion principle) very stable thanks to the occurrence of ‘paired spin’. On the other hand, nuclei with an odd number of protons and neutrons are mostly unstable.

Pauli Exclusion Principle and Neutron Stars

A neutron star is the collapsed core of a large star (usually of a red giant). Neutron stars are the smallest and densest stars known to exist and they are rotating extremely rapidly. A neutron star is basically a giant atomic nucleus about 11 km in diameter made especially of neutrons. It is believed that under the immense pressures of a collapsing massive stars going supernova it is possible for the electrons and protons  to combine to form neutrons via electron capture, releasing a huge amount of neutrinos. Since they have some similar properties as atomic nuclei, neutron stars are sometimes described as giant nuclei. But be careful, neutron stars and atomic nuclei are held together by different forces.  A nucleus is held together by the strong force, while a neutron star is held together by gravitational force.

On the other hand, neutron stars are partially supported against further collapse by neutron degeneracy (via degeneracy pressure), a phenomenon described by the Pauli exclusion principle. In general, in a highly dense state of matter, where gravitational pressure is extreme, quantum mechanical effects are significant. Degenerate matter is usually modelled as an ideal Fermi gas, in which the Pauli exclusion principle prevents identical fermions from occupying the same quantum state. Similarly, white dwarfs are supported against collapse by electron degeneracy pressure, which is analogous to neutron degeneracy.

References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See also:

Atomic Theory

We hope, this article, Pauli Exclusion Principle, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about materials and their properties.