Nucleus Structure

12 Key excerpts on "Nucleus Structure"

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  Fundamentals of Nuclear Models

  Foundational Models

  • David J Rowe, John L Wood;;;(Authors)
  • 2010(Publication Date)
  • WSPC

    (Publisher)

  Chapter 1 Elements of nuclear structure 1.1 Introduction A nucleus is the core of an atom. By atomic standards, its dimensions are minus-cule. Atoms have radii of the order of 10 − 9 m whereas nuclear radii are more like 10 − 14 m. Compared to an atom, a nucleus is like a grain of sand in a football sta-dium. Nevertheless, its mass is almost the entire mass of the atom. Approximately 99.97% of the mass of an atom resides in its nucleus. This means that, by mass, approximately 99.97% of the material world is nuclear matter. Nuclei consist of nucleons of which there are two types: positively charged pro-tons and uncharged neutrons. Both nucleon types have essentially the same mass and are approximately 2000 times as massive as an electron. They are held together in a nucleus by the so-called strong interaction . This interaction is much stronger but of much shorter range than the Coulomb interaction that binds the atomic electrons to their nuclei. At a separation distance of 1.0fm, the strong attraction between two nucleons is some 30 times as strong as the Coulomb repulsion between two protons. However, at a distance of 20fm, the strong interaction is smaller than the Coulomb interaction by a factor of 2000. In spite of the predominance of nuclear matter in our world, it is easy to be oblivious to the existence of nuclei. This is because nuclei are hidden beneath pro-tective clouds of atomic electrons which effectively keep them apart. In addition, nuclei are prevented from coming into contact with one another by the electro-static repulsions that result from their positive charges. Thus, one has little direct experience of nuclei outside of the nuclear physics laboratory. Because nuclei are so isolated, it is not surprising that most physical properties of the everyday world can be explained in terms of atoms and the electronic bonds they make with one another to form molecules and solids.

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  Fundamentals of Nuclear Physics

  • Ritesh Kohale, Sanjay J. Dhoble, Vibha Chopra(Authors)
  • 2009(Publication Date)
  • Bentham Science Publishers

    (Publisher)

  Nuclear Structure and Properties of Nuclei Ritesh Kohale , Sanjay J. Dhoble , Vibha Chopra

  Abstract

  An atom's nucleus comprises neutrons and protons, which in turn are the appearance of more fundamental particles, called quarks, that are seized in a relationship by the strong nuclear force in certain stable arrangements of hadrons, called baryons. The strong nuclear force encompasses far enough from each baryon to drag the neutrons and protons together beside the repulsive electrical force between the positively charged protons. The present chapter deals with investigating and correlating key features of the nuclear structure and its properties as understanding the structure of the atomic nucleus is one of the central challenges in nuclear physics. The line of understanding in this chapter is subjected to the structure of nuclei, atomic models, Rutherford model of the atom, nuclear composition, nuclear properties, determination of mass and determination of the charge.

  Keywords: Charge, Mass, Nuclear Properties, Nuclear Structure, Nuclear Structure.

  1. INTRODUCTION

  When discussing the atomic nucleus, it is very important to know about the history of the atom. An ‘Atom’ is the smallest particle of a substance that can exist by itself. Each atom consists of a nucleus with a positive charge and a set of electrons that move around the nucleus. The atom in its normal state is always found to be electrically neutral so that the number of protons and electrons must be exactly equal.

  The nucleus was revealed in 1911 due to Ernest Rutherford's determinations to test Thomson's “plum pudding model” of the atom [1

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  Introduction

  • Frank Rösch(Author)
  • 2014(Publication Date)
  • De Gruyter

    (Publisher)

  2 The atom’s structure II: Nucleons and nucleus

  Aim: While the first chapter recalled the principal composition of an atom, consisting of a nucleus and a shell with electrons of individual properties, this chapter introduces the principles and components of the atom’s Nucleus Structure. The nucleus contains protons and neutrons, the nucleons. Nuclei with the same number of protons but different numbers of neutrons create a rich world of isotopes of the same element. Every nucleus is described by a set of three numbers: the number of protons (identifying the chemical element), the number of neutrons (reflecting the specific isotope of that element), and the sum of protons and neutrons (forming the mass number). Analogously to the PSE for the chemical elements, the Chart of Nuclides arranges chemical properties of elements according to their electron shell parameters along with increasing mass of the element. The Chart of Nuclides correlates more than 3000 nuclei identified so far in an (x,y)-coordinate system with x = neutron number N and y = proton number Z.

   

  Masses and volumes (or radii) are the physical derivatives of every set of nucleons. Mass divided by volume gives the density of a nucleus – the density of matter. Radii may refer to (homogeneous) mass distribution within the nucleus’ volume, but also to charge distribution (which is the distribution of protons within the nucleus).

   

  Masses of individual nuclei are of ultimate interest, since mass equals energy. Exact knowledge of the precise mass of a nucleus provides access to the overall nucleon binding energy. Binding energies per nucleon determine to a significant extent the stability or non-stability of a given nucleus.

  2.1 The neutron

  With quantum mechanics, the one electron of the hydrogen atom was finally understood as energetically “surviving” in specific orbits of the shell. This electron is attracted by the one proton in the nucleus of the hydrogen atom. This particular atom has no other components. However, all the many other atoms of all other chemical elements contain an additional basic constituent – the neutron.

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  Modern Physics

  • Kenneth S. Krane(Author)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  Chapter 12 NUCLEAR STRUCTURE AND RADIOACTIVITY Radioactive isotopes have proven to be valuable tools for medical diagnosis. The photo shows gamma-ray emission from a patient who has been treated with a radioactive element. The radioactivity concentrates in locations where there are active cancer tumors, which show as bright areas in the gamma-ray scan. This patient’s cancer has spread from his prostate gland to several other locations in his body. GJLP, CNRI / Science Source 390 Chapter 12 Nuclear Structure and Radioactivity The nucleus lies at the center of the atom, occupying only 10 −15 of its vol- ume but providing the electrical force that holds the atom together. Within the nucleus there are Z positive charges. To keep these charges from flying apart, the nuclear force must supply an attraction that overcomes their electrical repulsion. This nuclear force is the strongest of the known forces; it provides nuclear binding energies that are millions of times stronger than atomic bind- ing energies. There are many similarities between atomic structure and nuclear structure, which will make our study of the properties of the nucleus somewhat famil- iar. Nuclei are subject to the laws of quantum physics. They have ground and excited states and emit photons in transitions between the excited states. Just like atomic states, nuclear states can be labeled by their angular momentum. There are, however, two major differences between the study of atomic and nuclear properties. In atomic physics, the electrons experience the force provided by an external agent, the nucleus; in nuclear physics, there is no such external agent.

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  Physics : Imagination And Reality

  • P R Wallace(Author)
  • 1991(Publication Date)
  • World Scientific

    (Publisher)

  Chapter 16 T H E A T O M I C N U C L E U S Its Constituents and Structure The atomic nucleus consists of two components, neutrons and protons, collectively called nucleons. These particles have very sim-ilar though not identical masses. The masses can be measured in energy units Mev/c 2 (million electron volts divided by the square of the speed of light). The neutron rest energy is 939.50 Mev. It has no charge. The rest-energy of the proton is 938.21 Mev. Its charge is equal and opposite to that of the electron. Strangely enough, al-though the neutron is overall electrically neutral, it has a magnetic moment, negative in value, of —1.9128 nuclear magnetons. The nu-clear magneton is eh/M p c where h is the modified Planck constant and M p , the proton mass. The magnetic moment of the proton is 2.7928 magnetons. Both of these values appear anomalous, and suggest a substructure for the two particles, as we shall see later. Some important properties of nuclei have been established ex-perimentally: 1. All nuclei, with the possible exception of the very lightest, have approximately the same density. If there are A nucleons in the nucleus, the volume of the nucleus is proportional to A. 2. When we speak of the volume of the nucleus, we imply that it has a fairly sharply denned radius. This appears to indicate that the range of the nuclear forces is quite short, and that the forces are strong. 3. Studies of nuclear reactions enable us to determine the bind-434 The Atomic Nucleus 435 ing energies of nucleons in the nucleus. These binding energies are found to be roughly independent of the size of the nucleus, that is, of A. 4. The total internal energy of the nucleus may be determined from the difference between its mass and the sums of the masses of its constituents. It is found that this does not rise systematically with the nuclear mass or nucleon number.

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  Modern Physics

  • Gary N. Felder, Kenny M. Felder(Authors)
  • 2022(Publication Date)
  • Cambridge University Press

    (Publisher)

  If you don’t have time in your course for the whole chapter, it would be perfectly reasonable to get the overview that Section 12.1 provides and stop there. Later sections discuss some of the experimental evidence for nuclear structure, nuclear models, and nuclear reactions. Chapter 13 takes the final step downward, to the particles that make up protons and neutrons. 12.1 What’s in a Nucleus? An atom is a small cluster of protons and neutrons, surrounded at a great distance by electrons. Chapters 7 and 8 talked about those electrons a lot: the energy levels they can occupy, transitions 556 12.1 What’s in a Nucleus? 557 between those levels, and so on. But those discussions treated the nucleus as a positively charged “black box” in the center. What do you see when you peer inside the box? 12.1.1 Discovery Exercise: What’s in a Nucleus? Two protons sit 10 −15 m away from each other. They are held together by the “strong nuclear force” but repel each other electrically. 1. Find the magnitude of the (positive) electric potential energy of the two protons. See Check Yourself #21 at www.cambridge.org/felder-modernphysics/checkyourself 2. For the protons to be bound in the nucleus, they must have a negative potential energy whose magnitude is larger than the electric potential energy you just calculated. To put that number in context, how many times larger is that electric potential energy than the 13.6 eV binding energy of an electron in a hydrogen atom? 12.1.2 Explanation: What’s in a Nucleus? A nucleus is a not-quite-spherical collection of positively charged protons and uncharged neutrons at the center of an atom. Each “nucleon” (proton or neutron) has about 2000 times the mass of an electron. But they’re not identical; a neutron is about 0.1% heavier than a proton.

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  Introduction to Nuclear Reactor Physics

  • Robert E. Masterson(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  a drop of incompressible fluid with an outer surface that undulates slightly as it moves. Classically, the diameter of the nucleus is given by the equation

  Equation for the Diameter of the Nucleus

  (2.12)

  D = 2.5

  A

  1 / 3

  ×

  10

  − 13

  cm

  where A is the

  Baryon number

  (the number of protons and neutrons) in the nucleus. The protons and neutrons may occasionally move across this boundary (e.g., during the process of electron capture), but on average, this is as far as the nuclear force field, which is carried by the gluons, can reach. Because the protons in the nucleus tend to repel each other due to their electric charge, they normally orbit closer to the edge of the nucleus than the neutrons do, and this fact is reflected in many modern models of nuclear structure (see Chapter 6 ).

  Example Problem 2.4 Suppose that the nucleus of an atom consists of 30 protons and 34 neutrons. What should the approximate diameter of the nucleus be?

  Solution According to Equation 2.12 , the diameter of the nucleus is D = 2.5A1/3 × 10−13 cm. Since the nucleus contains 30 protons and 34 neutrons, the atomic number is A = Z + N = 64. The diameter of the nucleus is therefore D = 2.5 × (64)1/3 × 10−13 cm = 2.5 × 4 × 10−13 cm = 1 × 10−12 cm. This particular combination happens to be an isotope of the element Zinc (Zn). [Ans].

  2.10Density of the Atomic Nucleus

  The nucleus is a very dense structure. In fact, it is millions of times denser than any other structure we know of in nature

  . The total mass of the nucleus mNUCLEUS can be written as the sum of the masses of the nucleons it contains. So to a first approximation, neglecting the binding forces, the mass of the nucleus is given by

  (2.13)

  m NUCLEUS

  = A ×

  m NUCLEON

  where A is the atomic number (the number of nucleons or the total number of protons Z and neutrons N):

  (2.14)

  A = Z + N

  and mNUCLEON is the average mass of a nucleon (about 1 AMU or 1.6605402 × 10−24 g = 1.6605402 × 10−27 kg). The density ρNUCLEUS of the nucleus (in kg/m3

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  The Quantum World of Nuclear Physics

  • Yuri A Berezhnoy(Author)
  • 2005(Publication Date)
  • WSPC

    (Publisher)

  Chapter 3 Structure of Atomic Nuclei 3.1 Composition and Properties of Nuclei In 1909 Geiger and Marsden, disciples of Rutherford, found that the most probable scattering angle of the 5.5 MeV.a-particles emitted by radioactive bismuth 214 Bi (called RaC at that time), and passing through gold foil 4 • 10~ 7 m thick, was 0.87°. However, approximately one a-particle in 20,000 was scattered at an angle exceeding 90°, i.e., backward. Rutherford's genius helped him understand this deviation of a small number of cc-particles through large angles. He argued that a positively charged a-particle with sufficiently high energy could be backscattered by a collision with something extremely small, heavy, and charged within the atom. He introduced the notion of atomic nucleus by analogy with the cell nucleus in biology. Rutherford made a simple calculation and found that the linear size of nucleus was at least thousand times smaller than that of the atom. The formula he obtained (which was later named after him) made it possible to describe the scattering of one charged point particle by another. Rutherford was extremely lucky because his formula, obtained on the basis of classical notions, turned out to be correct in quantum mechanics, too, which was understood much later. Therefore, in 1911 Rutherford drew the conclusion regarding the existence of an atomic nucleus. An atomic nucleus possesses fascinating properties. It contains approx-imately 99.97% of the atomic mass, but occupies a volume ten thousand billion times smaller than that of an atom. This means that the atom, as is the case with all matter, consists mostly of empty space. In other words, the density of nuclear matter is ten thousand billion times greater than the density of Earth matter. The carrying capacity of a single truck is sufficient 67 68 The Quantum World of Nuclear Physics to transport just 2 • 10~ 13 m 3 worth of nuclear matter.

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  Atoms, Radiation, and Radiation Protection

  • James S. Bogard, Darryl J. Downing, Robert L. Coleman, Keith F. Eckerman, James E. Turner(Authors)
  • 2022(Publication Date)
  • Wiley-VCH

    (Publisher)

  3 The Nucleus and Nuclear Radiation

  3.1 Nuclear Structure

  The nucleus of an atom of atomic number Z and mass number A consists of Z protons and N = A – Z neutrons. The atomic masses of all individual atoms are nearly integers, and A gives the total number of nucleons (i.e., protons and neutrons) in the nucleus. A species of atom, characterized by its nuclear constitution—its values of Z and A (or N)—is called a nuclide. It is conveniently designated by writing the appropriate chemical symbol with a subscript giving Z and superscript giving A. For example, and and are nuclides. Nuclides of an element that have different A (or N) are called isotopes; nuclides having the same number of neutrons are called isotones; for example, and are isotones with N = 124. Hydrogen has three isotopes, and all of which occur naturally. Deuterium, is stable; tritium, is radioactive. Fluorine has only a single naturally occurring isotope, all of its other isotopes are man-made, radioactive, and short lived. The measured atomic weights of the elements reflect the relative abundances of the isotopes found in nature, as the next example illustrates.

  Example

  Chlorine is found to have two naturally occurring isotopes: which is 76% abundant, and which is 24% abundant. The atomic weights of the two isotopes are 34.97 and 36.97. Show that this isotopic composition accounts for the observed atomic weight of the element.

  Solution

  Taking the weighted average of the atomic weights of the two isotopes, we find for the atomic weight of Cl, 0.76 × 34.97 + 0.24 × 36.97 = 35.45, as observed. (See periodic table in back of book.)

  Since the electron configuration of the different isotopes of an element is the same, isotopes cannot be separated chemically. The existence of isotopes does cause a very slight perturbation in atomic energy levels, leading to an observed “isotope shift” in some spectral lines. In addition, the different nuclear spins of different isotopes of the same element are responsible for hyperfine structure in the spectra of elements. As we mentioned at the end of Section 2.8

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  The Sciences

  An Integrated Approach

  • James Trefil, Robert M. Hazen(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  The atom, which has a diameter 100,000 times that of its nucleus, is almost entirely empty space. Previous chapters explored the properties of atoms in terms of their electrons. Chemical reactions, the way a material handles electricity, and even the very shape and strength of objects depend on the way that electrons in different atoms interact with each other. In terms of our analogy, all of the properties of the atoms that we have studied so far result from actions that are taking place 25 kilometers from the location of the basketball-sized nucleus. The incredible emptiness of the atom is a key to understanding two important facts about the relation of the atom to its nucleus. 1. The nucleus of an atom is largely unaffected by chemical reactions involving the atom’s electrons, and vice versa. The chemical bonding of an atom’s electrons has virtually no effect on what happens to the nucleus. In most situations you can regard the electrons and the central nucleus as two separate and independent systems. 2. The energies available in the nucleus are much greater than those available among electrons. The particles inside the nucleus are tightly locked in. Because most of the mass of the atom is in the nucleus, it shouldn’t be surprising that most of the energy resides there as well. It takes a great deal more energy to pull a proton or neutron from an atom than it does to remove an electron. The enormous energy we can get from the nucleus follows from the equivalence of mass and energy (which we discussed in Chapter 3). This relationship is defined in Einstein’s most famous equation. Radioactivity Around Us It’s great to be lying on the beach, lulled by the sound of the surf, soaking up the Sun. Away from the pressures of school and work, time seems to stand still. In such a relaxing setting it’s hard to imagine that hundreds of energetic radioactive particles are tearing through your body every minute.

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  Modern Physics for Scientists and Engineers

  • Stephen Thornton, Andrew Rex, Carol Hood, , Stephen Thornton, Stephen Thornton, Andrew Rex, Carol Hood(Authors)
  • 2020(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Copyright 2021 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 452 Chapter 12 The Atomic Nucleus Nuclear Models Physicists do not fully understand the nuclear force or how nucleons interact inside the nucleus. Current research focuses on the constituent quarks (see Chapter 14) that make up the nucleons. Because the nuclear force is not precisely known, physi- cists have relied on a multitude of models to explain nuclear behavior. These mod- els have been more or less successful in explaining various nuclear properties. The models generally fall into two categories: 1. Independent-particle models, in which the nucleons move nearly indepen- dently in a common nuclear potential. The shell model has been the most successful of these. 2. Strong-interaction models, in which the nucleons are strongly coupled to- gether. The liquid drop model already discussed is characteristic of these models and has been quite successful in explaining nuclear masses as well as nuclear fission (see Chapter 13). Space does not permit us a full discussion of each of the many models. We have already discussed the liquid drop model in this section, so we now present the simplest of the independent-particle models. We show in Figure 12.8 a representa- tion of the nuclear potential felt by the neutron and the proton. Because of the Coulomb interaction, the shape and depth of the proton potential is somewhat different than that of the neutron. For example, typical depths are about 43 MeV for neutrons but only 37 MeV for protons for medium to heavy nuclei.

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  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  However, if a person ingests a radioactive isotope of strontium, like 90 Sr, for example, then the isotope will settle in the bones and deliver harmful radiation to the nearby bone and marrow cells. This can lead to bone cancer and leukemia (Figure 31.19). If 90 Sr undergoes β − decay with a half-life of 29.1 years, what percentage of the initial amount is still in the body after 50.0 years? 906 CHAPTER 31 Nuclear Physics and Radioactivity Concept Summary 31.1 Nuclear Structure The nucleus of an atom consists of protons and neutrons, which are collectively referred to as nucleons. A neutron is an elec- trically neutral particle whose mass is slightly larger than that of the proton. The atomic number Z is the number of protons in the nucleus. The atomic mass number A (or nucleon number) is the total number of protons and neut- rons in the nucleus and is given by Equation 31.1, where N is the number of neutrons. For an element whose chemical symbol is X, the symbol for the nucleus is A Z X. Nuclei that contain the same number of protons, but a different number of neutrons, are called isotopes. The approximate radius (in meters) of a nucleus is given by Equation 31.2. A = Z + N (31.1) r ≈ (1.2 × 10 −15 m) A 1/3 (31.2) 31.2 The Strong Nuclear Force and the Stability of the Nucleus The strong nuclear force is the force of attraction between nucleons (protons and neutrons) and is one of the three fundamental forces of nature. This force balances the electrostatic force of repulsion between protons and holds the nucleus together. The strong nuclear force has a very short range of action and is almost independent of electric charge. 31.3 The Mass Defect of the Nucleus and Nuclear Binding Energy The binding energy of a nucleus is the energy required to separate the nucleus into its constituent protons and neutrons. The binding energy is given by Equation 31.3, where Δm is the mass defect of the nucleus and c is the speed of light in a vacuum.

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