31.1

Nuclear Structure

Atoms consist of electrons in orbit about a central nucleus. As we have seen in Chapter 30, the electron orbits are quantum mechanical in nature and have interesting characteristics. Little has been said about the nucleus, however. Since the nucleus is interesting in its own right, we now consider it in greater detail.
The nucleus of an atom consists of neutrons and protons, collectively referred to as nucleons. The neutron, discovered in 1932 by the English physicist James Chadwick (1891–1974), carries no electric charge and has a mass slightly larger than that of a proton (see Table 31-1).

Table 31-1 Properties of Select Particles

|  | Mass
Particle | Electric Charge (C) | Kilograms (kg) | Atomic Mass Units (u)
Eectron |  |  |
Proton |  |  | 1.007 276
Neutron | 0 |  | 1.008 665
Hydrogen atom | 0 |  | 1.007 825

The number of protons in the nucleus is different in different elements and is given by the atomic number Z. In an electrically neutral atom, the number of nuclear protons equals the number of electrons in orbit around the nucleus. The number of neutrons in the nucleus is N. The total number of protons and neutrons is referred to as the atomic mass number A because the total nuclear mass is approximately equal to A times the mass of a single nucleon:

| (31.1)

Sometimes A is also called the nucleon number. A shorthand notation is often used to specify Z and A along with the chemical symbol for the element. For instance, the nuclei of all naturally occurring aluminum atoms have , and the atomic number for aluminum is . In shorthand notation, then, the aluminum nucleus is specified as . The number of neutrons in an aluminum nucleus . In general, for an element whose chemical symbol is X, the symbol for the nucleus is

For a proton the symbol is , since the proton is the nucleus of a hydrogen atom. A neutron is denoted by . In the case of an electron we use , where because an electron is not composed of protons or neutrons and because the electron has a negative charge.
Nuclei that contain the same number of protons, but a different number of neutrons, are known as isotopes. Carbon, for example, occurs in nature in two stable forms. In most carbon atoms (98.90%), the nucleus is the isotope and consists of six protons and six neutrons. A small fraction (1.10%), however, contain nuclei that have six protons and seven neutrons, namely, the isotope. The percentages given here are the natural abundances of the isotopes. The atomic masses in the periodic table are average atomic masses, taking into account the abundances of the various isotopes.
The protons and neutrons in the nucleus are clustered together to form an approximately spherical region, as Figure 31-1 illustrates. Experiment shows that the radius r of the nucleus depends on the atomic mass number A and is given approximately in meters by

| (31.2)

The radius of the aluminum nucleus (), for example, is . Equation 31.2 leads to an important conclusion concerning the nuclear density of different atoms, as Conceptual Example 1 discusses.

Figure 31-1 The nucleus is approximately spherical (radius = r) and contains protons clustered closely together with neutrons .

| Conceptual Example 1 | | | Nuclear Density

It is well known that lead and oxygen contain different atoms and that the density of solid lead is much greater than that of gaseous oxygen. Using Equation 31.2, decide whether the density of the nucleus in a lead atom is greater than, approximately equal to, or less than that in an oxygen atom.
Reasoning and Solution We know from Equation 11.1 that density is mass divided by volume. The total mass M of a nucleus is approximately equal to the number of nucleons A times the mass m of a single nucleon, since the masses of a proton and a neutron are nearly the same: . The values of A are different for lead and oxygen atoms, however. The volume V of the nucleus is approximately spherical and has a radius r, so that . But is proportional to the number of nucleons A, as we can see by cubing each side of Equation 31.2. Therefore, the volume V is also proportional to A. Thus, when the total mass M is divided by the volume V, the factor of A appears in both the numerator and denominator and is eliminated algebraically from the result, no matter what the value of A is. We find, then, that the density of the nucleus in a lead atom is approximately the same as it is in an oxygen atom. In general, Equation 31.2 implies that the nuclear density has nearly the same value in all atoms. The difference in densities between solid lead and gaseous oxygen arises mainly because of the difference in how closely the atoms themselves are packed together in the solid and gaseous phases.
Related Homework: Problems 8 and 9

Check Your Understanding 1

Two nuclei have different numbers of protons and different numbers of neutrons. Which one or more of the following statements are true? (a) They are different isotopes of the same element. (b) They have the same electric charge. (c) They could have the same radii. (d) They have approximately the same nuclear density. (The answer is given at the end of the book.)
Background: Whether or not a nucleus belongs to a certain element depends on the atomic number of the nucleus. The radius and mass of a nucleus depend on its atomic mass number.
For similar questions (including calculational counterparts), consult Self-Assessment Test 31.1, which is described at the end of Section 31.5.

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