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ย ะง^ + ย .F
ย ะง^ +
.F
Finally, we determine the binding energy per nucleon by dividing the total nuclear binding energy by the number of nucleons in the atom:
#JOEJOHFOFSHZQFSOVDMFPO .F7 .F7OVDMFPO
Note that this is almost 25% larger than the binding energy per nucleon for (^) ^ )F
(Note also that this is the same process as in Example 21.1 , but with the additional step of dividing the total nuclear binding energy by the number of nucleons.) Check Your Learning What is the binding energy per nucleon in ^ ' (atomic mass, 18.9984 amu)?
Answer: 7.810 MeV/nucleon
21.2 Nuclear Equations
By the end of this section, you will be able to:
- Identify common particles and energies involved in nuclear reactions
- Write and balance nuclear equations
Changes of nuclei that result in changes in their atomic numbers, mass numbers, or energy states are nuclear reactions. To describe a nuclear reaction, we use an equation that identifies the nuclides involved in the reaction, their mass numbers and atomic numbers, and the other particles involved in the reaction.
Types of Particles in Nuclear Reactions
Many entities can be involved in nuclear reactions. The most common are protons, neutrons, alpha particles, beta particles, positrons, and gamma rays, as shown in Figure 21.4. Protons (^13) ^ Q also represented by the symbol
(^) )^46 and neutrons (^13)
(^) O^46 are the constituents of atomic nuclei, and have been described previously. Alpha particles 1 (^3) ^ )F^ also represented by the symbol^ ^ ษฐ
4 6 are high-energy helium nuclei.^ Beta particles^
1 3 ะง
(^) ษฑ also represented
by the symbol (^) ะง^ F^46 are high-energy electrons, and gamma rays are photons of very high-energy electromagnetic
radiation. Positrons^13 ^ F also represented by the symbol ^ ษฑ^46 are positively charged electrons (โanti-electronsโ).
The subscripts and superscripts are necessary for balancing nuclear equations, but are usually optional in other circumstances. For example, an alpha particle is a helium nucleus (He) with a charge of +2 and a mass number of 4, so it is symbolized (^) ^ )F This works because, in general, the ion charge is not important in the balancing of nuclear
equations.
Figure 21.4 Although many species are encountered in nuclear reactions, this table summarizes the names, symbols, representations, and descriptions of the most common of these.
Note that positrons are exactly like electrons, except they have the opposite charge. They are the most common example of antimatter , particles with the same mass but the opposite state of another property (for example, charge) than ordinary matter. When antimatter encounters ordinary matter, both are annihilated and their mass is converted into energy in the form of gamma rays (ฮณ) โand other much smaller subnuclear particles, which are beyond the scope of this chapterโaccording to the mass-energy equivalence equation E = mc^2 , seen in the preceding section. For example, when a positron and an electron collide, both are annihilated and two gamma ray photons are created:
ะง
F
(^) F ฺฎ ษฒ ษฒ
As seen in the chapter discussing light and electromagnetic radiation, gamma rays compose short wavelength, high- energy electromagnetic radiation and are (much) more energetic than better-known X-rays that can behave as particles in the wave-particle duality sense. Gamma rays are produced when a nucleus undergoes a transition from a higher to a lower energy state, similar to how a photon is produced by an electronic transition from a higher to a lower energy level. Due to the much larger energy differences between nuclear energy shells, gamma rays emanating from a nucleus have energies that are typically millions of times larger than electromagnetic radiation emanating from electronic transitions.
Balancing Nuclear Reactions
A balanced chemical reaction equation reflects the fact that during a chemical reaction, bonds break and form, and atoms are rearranged, but the total numbers of atoms of each element are conserved and do not change. A balanced nuclear reaction equation indicates that there is a rearrangement during a nuclear reaction, but of subatomic particles rather than atoms. Nuclear reactions also follow conservation laws, and they are balanced in two ways:
- The sum of the mass numbers of the reactants equals the sum of the mass numbers of the products.
- The sum of the charges of the reactants equals the sum of the charges of the products.
If the atomic number and the mass number of all but one of the particles in a nuclear reaction are known, we can identify the particle by balancing the reaction. For instance, we could determine that ^0 is a product of the nuclear
reaction of ^ / and (^) ^ )F if we knew that a proton, (^) ^ ) was one of the two products. Example 21.4 shows how
we can identify a nuclide by balancing the nuclear reaction.
This OpenStax book is available for free at http://cnx.org/content/col11760/1.
