Mass-energy relationships in nuclei

Recall from Section 1.4 that almost all the mass of an atom is concentrated in a very small volume in the nucleus. The small size of the nucleus (which occupies less than one trillionth of the space in the atom) and the strong forces between the protons and neutrons that make it up largely isolate its behavior from the outside world of electrons and other nuclei. This greatly simplifies our analysis of nuclear chemistry, allowing us to examine single nuclei without concern for the atoms, ions, or molecules in which they may be found. 

As defined in Section 1.4, a nuclide is characterized by the number of protons, Z, and the number of neutrons, N, it contains. The atomic number Z determines the charge -l- Ze on the nucleus and therefore decides the identity of the element the sum Z + N = A s the mass number of the nuclide and is the integer closest to the relative atomic mass of the nuclide. Nuclides are designated by the symbol zX where X is the chemical symbol for the element. 

The conversion factor between atomic mass units and grams is numerically equal to the inverse of Avogadro s number Na, and the mass of a single atom in atomic mass units is numerically equal to the mass of one mole of atoms in grams. Thus, one atom of has a mass of 1.007825 u because 1 mol of has a mass of 1.007825 g. The dalton is a mass unit that is equivalent to the atomic mass unit and is used frequently in biochemistry. 

TABLE 19.1 Masses of Selected Elementary Particles and Atoms 

Note from Table 19.1 that the neutron has a slightly greater mass than the proton. The neutron is stable inside a nucleus, but in free space it is unstable, decaying into a proton and an electron with a half-life of about 12 minutes  

---

Nuclear chemistry represents a particularly simple limiting form of kinetics in which unstable nuclei decay with a constant probability during anytime interval. Its richness arises from the multiplicity of decay paths that are possible, which arise from the mass-energy relationships that determine nuclear stability. 

The relationship of energy and mass would indicate that in the formation of deuterium by the combination of a proton and neutron, the mass defect of 0.002 388 u would be observed as the liberation of an equivalent amount of energy, i.e. 931.5 X 0.002 388 = 2.224 MeV. Indeed, the emission of this amount of energy (in the form of y-rays) is observed when a proton captures a low ergy neutron to form jH. As a matter of fact, in this particular case, the energy liberated in the formation of deuterium has been used in the reverse calculation to obtain the mass of the neutron since it is not possible to determine directly the mass of the free neutron. With the definition (3.2) all stable nuclei are found to have negative AAf values thus the term "defect". 

Reactions between an atomic nucleus and another particle are called nuclear reactions. In some such reactions, new nuclei are formed nuclear transmutations) in others the original nucleus is excited to a higher energy state (inelastic scattering) in a third class, the nucleus is unchanged (elasticscattering). Spontaneous nuclear transformations, which are involved in the radioactive decay of unstable nuclei, have be discussed in Chapter 4. In this chapter the enqrhasis is on the mass and energy relationships when a projectile interacts with a nucleus. 

SECTION 21.6 The energy produced in nuclear reactions is accompanied by measurable changes of mass in accordance with Einstein s relationship, A = Am. The difference in mass between nuclei and... 

Section 21.6 The energy produced in nuclear reactions is accompanied by measurable tosses of mass in accordance wilh Einstein s relationship, AE = c Am. The difference in mass between nuclei and the nucleons of which Ihey are composed is known as Ihe mass defect. The mass defect of a nuclide makes it possible to calculate its nuclear binding energy, Ihe energy required to separate Ihe nucleus into individual nucleons. Energy is produced when heavy nuclei split (fission) and when light nuclei fuse (fusion). 

One of the most important nuclear properties that can be measured is the mass. Nuclear or atomic masses are usually given in atomic mass units (amu or u) or their energy equivalent. The mass unit u is defined so that the mass of one atom of 12C is equal to 12.0000. .. u. Note we said atom. For convenience, the masses of atoms rather than nuclei are used in all calculations. When needed, the nuclear mass mllucl can be calculated from the relationship... 

It is not necessary to be able to perform these calculations for the AP test. However, it is very important that you understand the underlying idea that large amounts of energy are released when atomic nuclei are broken apart. It is also important to understand that the difference in mass between the components of a nucleus and the actual mass of the nucleus can be accounted for by a change in the energy state of those components. The nature of that relationship is captured in Einstein s equation E = me . 

---