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Figure 2.1 Simplified model atom with nucleus that contains positively charged protons (dark blue) and electrically neutral neutrons (light blue) surrounded by an electron cloud (red shades) in which negatively charged electrons move in orbitals about the nucleus.

      2.1.1 The nucleus, atomic number, atomic mass number, and isotopes

      The nucleus of atoms is composed of positively charged protons and uncharged neutrons bound together by a strong force. Ninety‐two fundamentally different kinds of atoms called elements have been discovered in the natural world. More than 25 additional elements have been created synthetically in laboratory experiments during the past century. Each element is characterized by the number of protons in its nucleus. The number of protons in the nucleus is called the atomic number (Z). The atomic number is typically represented by a subscript number to the lower left of the element symbol. The 92 naturally occurring elements range from hydrogen (Z = 1) through uranium (Z = 92). Hydrogen (₁H) is characterized by having one proton in its nucleus. Every atom of uranium (₉₂U) contains 92 protons in its nucleus. The atomic number is the unique property that distinguishes the atoms of each element from atoms of all other elements.

Every atom also possesses mass that largely results from the protons and neutrons in its nucleus. The mass of a particular atom is called its atomic mass number, and is expressed in atomic mass units (amu). As the mass of both protons and neutrons is ~1 amu, the atomic mass number is closely related to the total number of protons plus neutrons in its nucleus. The simple formula for atomic mass number is: atomic mass number = number of protons plus number of neutrons (#p⁺ + #n⁰). The atomic mass number is indicated by a superscript number to the upper left of the element symbol. For example, most oxygen atoms have eight protons and eight neutrons so their atomic mass number is written¹⁶O.

Although each element has a unique atomic number, many elements are characterized by atoms with different atomic mass numbers. Atoms of the same element that possess different atomic mass numbers are called isotopes. For example, three different isotopes of hydrogen exist (Figure 2.2a). All hydrogen (₁H) atoms have an atomic number of 1. The common form of hydrogen atom, sometimes called protium, has one proton and no neutrons in the nucleus; therefore protium has an atomic mass number of 1, symbolized as¹H. A less common form of hydrogen called deuterium, used in some nuclear reactors, has an atomic mass number of 2, symbolized by²H. This implies that it contains one proton and one neutron in its nucleus (1p⁺ + 1n⁰). A rarer isotope of hydrogen called tritium has an atomic mass number of 3, symbolized by³H. The nucleus of tritium has one proton and two neutrons. Similarly oxygen occurs in three different isotopes:¹⁶O,¹⁷O, and¹⁸O. All oxygen atoms contain eight protons but neutron numbers vary between¹⁶O,¹⁷O, and¹⁸O, which contain eight, nine, and ten neutrons, respectively (Figure 2.2a). The average atomic mass for each element is the weighted average for all the isotopes of that element. This helps to explain why the listed atomic masses for each element do not always approximate the whole numbers produced when one adds the number of protons and neutrons in the nucleus of a particular isotope.

Figure 2.2 (a) Nuclear configurations of the three common isotopes of hydrogen. (b) Nuclear configurations of the three common isotopes of oxygen.

      The general isotope symbol for the nucleus of an atom expresses its atomic number to the lower left of its symbol, the number of neutrons to the lower right and the atomic mass number (number of protons + number of neutrons) to the upper left. For example, the most common isotope of uranium has the symbolic nuclear configuration of 92 protons + 146 neutrons and an atomic mass number of 238:

      Stable isotopes have stable nuclear configurations that tend to remain unchanged; they retain the same number of protons and neutrons over time. On the other hand, radioactive isotopes have unstable nuclear configurations (numbers of protons and neutrons) that spontaneously change over time via radioactive decay processes, until they achieve stable nuclear configurations and become stable isotopes of another element. Both types of isotopes are extremely useful in solving geological and environmental problems, as discussed in Chapter 3. Radioactive isotopes are used in many medical treatments, but also present serious environmental hazards (Chapter 19).

      2.1.2 The electron cloud

Electrons are enigmatic entities, with properties of both particles and wave energy, that move very rapidly around the nucleus in ultimately unpredictable paths. Our depiction of the electron cloud is based on the probabilities of finding a particular electron at a particular place. The wave‐like properties of electrons help to define the three‐dimensional shapes of their probable locations, known as orbitals. The size and shape of the electron cloud defines the chemical behavior of atoms and ultimately the composition of all the Earth materials they combine to form. Simplified models of the electron cloud depict electrons distributed in spherical orbits around the nucleus (Figure 2.3); the reality is much more complex. Because the electron cloud largely determines the chemical behavior of atoms and how they combine to produce Earth materials, it is essential to understand some fundamental concepts about it.

Figure 2.3 Distribution of electrons in the principal quantum levels (“electron shells”) of uranium: K‐shell electrons violet; L‐shell blue; M‐shell bluish green; N‐shell green; O‐shell yellow; P‐shell orange and Q‐shell red.

      Every electron in an atom possesses a unique set of properties that distinguishes it from all the other electrons in that atom. An individual electron's identity is given by four properties that include its (1) principal quantum number, (2) azimuthal quantum number, (3) magnetic quantum number, and (4) spin number. Each electron in the electron cloud possesses a unique combination of the four quantum properties.

      The principal quantum number (n) signifies the principal quantum energy region, sometimes called “level” or “shell ” in which a particular electron occurs. It is related to its distance from the nucleus. Principle quantum regions are numbered in order of increasing electron energies 1, 2, 3, 4, 5, 6 or 7 or alternatively lettered K, L, M, N, O, P or Q. These are arranged from low principal quantum number for low energy regions closer to the nucleus to progressively higher quantum number for higher energy regions farther away from the nucleus.

Each principal quantum region or level contains electrons with one or more azimuthal or angular momentum quantum numbers

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