Which of the Following Nuclei Would Be the Least Stable

Which of the Following Nuclei Would Be the Least Stable.

21.2: Patterns of Nuclear Stability

  • Page ID
    21806
  • Learning Objectives
    • To empathize the factors that impact nuclear stability.

    Although virtually of the known elements have at least one isotope whose atomic nucleus is stable indefinitely, all elements have isotopes that are unstable and atomize, or disuse, at measurable rates by emitting radiation. Some elements take no stable isotopes and eventually decay to other elements. In contrast to the chemical reactions that were the main focus of before capacity and are due to changes in the arrangements of the valence electrons of atoms, the process of nuclear disuse results in changes inside an diminutive nucleus. We begin our give-and-take of nuclear reactions past reviewing the conventions used to describe the components of the nucleus.

    The Diminutive Nucleus

    Each element can be represented past the notation \(^A_Z \textrm Ten\), where
    A, the mass number, is the sum of the number of protons and the number of neutrons, and
    Z, the atomic number, is the number of protons. The protons and neutrons that brand up the nucleus of an atom are called
    nucleons, and an atom with a item number of protons and neutrons is called a
    nuclide. Nuclides with the same number of protons but unlike numbers of neutrons are called
    isotopes. Isotopes can besides be represented by an culling notation that uses the name of the chemical element followed by the mass number, such as carbon-12. The stable isotopes of oxygen, for example, can exist represented in whatever of the following ways:

    stable isotopes of oxygen represented in dissimilar ways
    \(^A_Z \textrm 10\) \(\ce{^{sixteen}_8 O}\) \(\ce{^{17}_8 O}\) \(\ce{^{18}_8 O}\)
    \(^A \textrm X\) \(\ce{^{16} O}\) \(\ce{^{17} O}\) \(\ce{^{18} O}\)
    \(\textrm{element-A:}\) \(\textrm{oxygen-xvi}\) \(\textrm{oxygen-17}\) \(\textrm{oxygen-18}\)

    Because the number of neutrons is equal to
    A

    Z, we run across that the commencement isotope of oxygen has 8 neutrons, the second isotope nine neutrons, and the 3rd isotope 10 neutrons. Isotopes of all naturally occurring elements on Earth are present in most fixed proportions, with each proportion constituting an isotope’s
    natural abundance. For instance, in a typical terrestrial sample of oxygen, 99.76% of the O atoms is oxygen-16, 0.20% is oxygen-eighteen, and 0.04% is oxygen-17. Whatever nucleus that is unstable and decays spontaneously is said to be
    radioactive, emitting subatomic particles and electromagnetic radiation. The emissions are collectively chosen
    radioactivity
    and tin be measured. Isotopes that emit radiation are called
    radioisotopes.

    Nuclear Stability

    The nucleus of an cantlet occupies a tiny fraction of the volume of an cantlet and contains the number of protons and neutrons that is characteristic of a given isotope. Electrostatic repulsions would normally crusade the positively charged protons to repel each other, but the nucleus does not fly apart because of the
    potent nuclear force, an extremely powerful but very brusk-range bonny force between nucleons (Figure \(\PageIndex{ane}\)). All stable nuclei except the hydrogen-one nucleus (iH) contain at to the lowest degree one neutron to overcome the electrostatic repulsion between protons. As the number of protons in the nucleus increases, the number of neutrons needed for a stable nucleus increases even more rapidly. As well many protons (or too few neutrons) in the nucleus outcome in an imbalance between forces, which leads to nuclear instability.

    Figure \(\PageIndex{ane}\): Competing Interactions within the Atomic Nucleus. Electrostatic repulsions between positively charged protons would ordinarily cause the nuclei of atoms (except H) to wing apart. In stable atomic nuclei, these repulsions are overcome by the strong nuclear force, a brusque-range only powerful attractive interaction between nucleons. If the attractive interactions due to the strong nuclear force are weaker than the electrostatic repulsions betwixt protons, the nucleus is unstable, and information technology volition eventually decay.

    The relationship between the number of protons and the number of neutrons in stable nuclei, arbitrarily defined equally having a one-half-life longer than 10 times the age of Earth, is shown graphically in
    Figure \(\PageIndex{2}\). The stable isotopes course a “peninsula of stability” in a “sea of instability.” Only two stable isotopes,
    oneH and
    threeHe, have a neutron-to-proton ratio less than one. Several stable isotopes of light atoms accept a neutron-to-proton ratio equal to ane (east.g., \(^4_2 \textrm{He}\), \(^{10}_5 \textrm{B}\), and \(^{40}_{xx} \textrm{Ca}\)). All other stable nuclei have a higher neutron-to-proton ratio, which increases steadily to well-nigh 1.5 for the heaviest nuclei. Regardless of the number of neutrons, yet, all elements with Z > 83 are unstable and radioactive.

    Figure \(\PageIndex{2}\): The Relationship between Nuclear Stability and the Neutron-to-Proton Ratio. In this plot of the number of neutrons versus the number of protons, each black point corresponds to a stable nucleus. In this classification, a stable nucleus is arbitrarily defined equally one with a one-half-life longer than 46 billion years (10 times the historic period of Earth). As the number of protons (the diminutive number) increases, the number of neutrons required for a stable nucleus increases fifty-fifty more speedily. Isotopes shown in ruby-red, yellowish, green, and blueish are progressively less stable and more radioactive; the farther an isotope is from the diagonal band of stable isotopes, the shorter its one-half-life. The purple dots indicate superheavy nuclei that are predicted to be relatively stable, meaning that they are expected to exist radioactive but to have relatively long half-lives. In well-nigh cases, these elements have not yet been observed or synthesized. Data source: National Nuclear Information Heart, Brookhaven National Laboratory, Evaluated Nuclear Structure Data File (ENSDF), Nautical chart of Nuclides, http://world wide web.nndc.bnl.gov/chart.
    Graph of number or neutrons confronting the number or protons. The graph is divided into sections of “body of water of instability”, “peninsula of stability”, “sea of instability” and “isle of stability”

    As shown in
    Figure \(\PageIndex{3}\), more than half of the stable nuclei (166 out of 279) have
    fifty-fifty
    numbers of both neutrons and protons; merely six of the 279 stable nuclei exercise not have odd numbers of both. Moreover, certain numbers of neutrons or protons result in specially stable nuclei; these are the so-called
    magic numbers
    2, eight, xx, l, 82, and 126. For case, tin (Z
    = 50) has 10 stable isotopes, merely the elements on either side of tin in the periodic table, indium (Z
    = 49) and antimony (Z
    = 51), have simply ii stable isotopes each. Nuclei with magic numbers of
    both
    protons
    and
    neutrons are said to exist “doubly magic” and are fifty-fifty more stable. Examples of elements with doubly magic nuclei are \(^4_2 \textrm{He}\), with 2 protons and two neutrons, and \(^{208}_{82} \textrm{Pb}\), with 82 protons and 126 neutrons, which is the heaviest known stable isotope of any chemical element.

    Bar graph of number of stable nuclei against neutrons and protons. The highest number or stable nuclei is when the number or neutrons and protons are both even. The second highest number of stable nuclei is when the number of neutrons is odd and the number of protons is even. The third highest number or stable nucei si when the number or neutrons is even and the number of protons is odd. The lowest number of stable nuclei is when the number of neutrons and protons are both odd.
    Figure \(\PageIndex{3}\): The Relationship between the Number of Protons and the Number of Neutrons and Nuclear Stability.

    Most stable nuclei contain
    even
    numbers of both neutrons and protons

    The pattern of stability suggested past the magic numbers of nucleons is reminiscent of the stability associated with the closed-shell electron configurations of the noble gases in group 18 and has led to the hypothesis that the nucleus contains shells of nucleons that are in some ways analogous to the shells occupied past electrons in an atom. As shown in
    Figure \(\PageIndex{2}\), the “peninsula” of stable isotopes is surrounded by a “reef” of radioactive isotopes, which are stable enough to exist for varying lengths of time earlier they eventually disuse to produce other nuclei.

    Origin of the Magic Numbers

    Multiple models have been formulated to explain the origin of the magic numbers and two popular ones are the Nuclear Vanquish Model and the Liquid Drop Model. Unfortuneatly, both require advanced quantum mechanics to fully understand and are beyond the scope of this text.

    Example \(\PageIndex{1}\)

    Classify each nuclide as stable or radioactive.

    1. \(\ce{_{15}^{30} P}\)
    2. \(\ce{_{43}^{98} Tc}\)
    3. tin can-118
    4. \(\ce{_{94}^{239} Pu}\)

    Given: mass number and atomic number

    Asked for: predicted nuclear stability

    Strategy:

    Employ the number of protons, the neutron-to-proton ratio, and the presence of fifty-fifty or odd numbers of neutrons and protons to predict the stability or radioactive decay of each nuclide.

    Solution:

    a. This isotope of phosphorus has 15 neutrons and fifteen protons, giving a neutron-to-proton ratio of 1.0. Although the atomic number, xv, is much less than the value of 83 above which all nuclides are unstable, the neutron-to-proton ratio is less than that expected for stability for an chemical element with this mass. As shown in
    Effigy \(\PageIndex{2}\), its neutron-to-proton ratio should exist greater than 1. Moreover, this isotope has an odd number of both neutrons and protons, which too tends to brand a nuclide unstable. Consequently, \(_{15}^{30} \textrm P\) is predicted to be radioactive, and it is.

    b. This isotope of technetium has 55 neutrons and 43 protons, giving a neutron-to-proton ratio of i.28, which places \(_{43}^{98} \textrm{Tc}\) near the edge of the ring of stability. The atomic number, 55, is much less than the value of 83 above which all isotopes are unstable. These facts suggest that \(_{43}^{98} \textrm{Tc}\) might be stable. However, \(_{43}^{98} \textrm{Tc}\) has an odd number of both neutrons and protons, a combination that seldom gives a stable nucleus. Consequently, \(_{43}^{98} \textrm{Tc}\) is predicted to be radioactive, and information technology is.

    c. Tin can-118 has 68 neutrons and 50 protons, for a neutron-to-proton ratio of 1.36. Equally in part b, this value and the diminutive number both suggest stability. In improver, the isotope has an fifty-fifty number of both neutrons and protons, which tends to increase nuclear stability. Most of import, the nucleus has 50 protons, and 50 is 1 of the magic numbers associated with particularly stable nuclei. Thus \(_{50}^{118} \textrm{Sn}\)should be particularly stable.

    d. This nuclide has an atomic number of 94. Because all nuclei with Z > 83 are unstable, \(_{94}^{239} \textrm{Pu}\) must be radioactive.

    Exercise \(\PageIndex{i}\)

    Allocate each nuclide as stable or radioactive.

    1. \(\ce{_{xc}^{232} Th}\)
    2. \(\ce{_{20}^{twoscore} Ca}\)
    3. \(\ce{_8^{15} O}\)
    4. \(\ce{_{57}^{139} La}\)
    Respond a

    radioactive

    Answer b

    stable

    Answer c

    radioactive

    Respond d

    stable

    Superheavy Elements

    In addition to the “peninsula of stability” there is a modest “island of stability” that is predicted to exist in the upper right corner. This island corresponds to the
    superheavy elements, with atomic numbers virtually the magic number 126. Because the next magic number for neutrons should exist 184, information technology was suggested that an chemical element with 114 protons and 184 neutrons might be stable enough to be in nature. Although these claims were met with skepticism for many years, since 1999 a few atoms of isotopes with
    Z
    = 114 and
    Z
    = 116 have been prepared and found to be surprisingly stable. Ane isotope of element 114 lasts two.7 seconds before decomposable, described as an “eternity” by nuclear chemists. Moreover, there is contempo evidence for the existence of a nucleus with
    A
    = 292 that was found in
    232Th. With an estimated half-life greater than x8
    years, the isotope is particularly stable. Its measured mass is consistent with predictions for the mass of an isotope with
    Z
    = 122. Thus a number of relatively long-lived nuclei may well be accessible among the superheavy elements.

    Summary

    Subatomic particles of the nucleus (protons and neutrons) are called
    nucleons. A
    nuclide
    is an atom with a particular number of protons and neutrons. An unstable nucleus that decays spontaneously is
    radioactive, and its emissions are collectively called
    radioactive decay. Isotopes that emit radiation are called
    radioisotopes. Each nucleon is attracted to other nucleons past the
    strong nuclear strength. Stable nuclei generally have even numbers of both protons and neutrons and a neutron-to-proton ratio of at least 1. Nuclei that contain
    magic numbers
    of protons and neutrons are often peculiarly stable.
    Superheavy elements, with atomic numbers near 126, may fifty-fifty be stable enough to be in nature.

    Which of the Following Nuclei Would Be the Least Stable

    Source: https://chem.libretexts.org/Bookshelves/General_Chemistry/Map:_Chemistry_-_The_Central_Science_%28Brown_et_al.%29/21:_Nuclear_Chemistry/21.02:_Patterns_of_Nuclear_Stability