Using this mass-energy equivalence equation, the nuclear binding energy of a nucleus may be calculated from its mass defect, as demonstrated in Example 2. Determine the binding energy in joules per nuclide using the mass-energy equivalence equation. The mass defect is therefore 0. Converting grams into kilograms yields a mass defect of 3. Substituting this quantity into the mass-energy equivalence equation yields:.
Note that this tremendous amount of energy is associated with the conversion of a very small amount of matter about 30 mg, roughly the mass of typical drop of water. Using the binding energy computed in part b :. Because the energy changes for breaking and forming bonds are so small compared to the energy changes for breaking or forming nuclei, the changes in mass during all ordinary chemical reactions are virtually undetectable. A nucleus is stable if it cannot be transformed into another configuration without adding energy from the outside.
Of the thousands of nuclides that exist, about are stable. A plot of the number of neutrons versus the number of protons for stable nuclei reveals that the stable isotopes fall into a narrow band.
This region is known as the band of stability also called the belt, zone, or valley of stability. The straight line in Figure 1 represents nuclei that have a ratio of protons to neutrons n:p ratio. Note that the lighter stable nuclei, in general, have equal numbers of protons and neutrons.
For example, nitrogen has seven protons and seven neutrons. Heavier stable nuclei, however, have increasingly more neutrons than protons.
For example: iron has 30 neutrons and 26 protons, an n:p ratio of 1. This is because larger nuclei have more proton-proton repulsions, and require larger numbers of neutrons to provide compensating strong forces to overcome these electrostatic repulsions and hold the nucleus together. The nuclei that are to the left or to the right of the band of stability are unstable and exhibit radioactivity.
They change spontaneously decay into other nuclei that are either in, or closer to, the band of stability. These nuclear decay reactions convert one unstable isotope or radioisotope into another, more stable, isotope. We will discuss the nature and products of this radioactive decay in subsequent sections of this chapter. They are a variant of a basic element. For example, there are three isotopes or variants of hydrogen: hydrogen-1 one proton and no neutrons , hydrogen-2 or deuterium one proton and one neutron , and hydrogen-3 which is called tritium one proton and two neutrons.
Another example is uranium which has 92 protons and neutrons, and uranium which has 92 protons and neutrons. Both uranium and uranium are isotopes of uranium. Many isotopes are stable. They will not undergo radioactive decay and give off radiation. Other isotopes are not stable. An isotope is stable when there is a balance between the number of neutrons and protons. When an isotope is small and stable, it contains close to an equal number of protons and neutrons. Isotopes that are larger and stable have slightly more neutrons than protons.
An example of a stable isotope is carbon, which has six protons and six neutrons, for a total mass of 12g. When there is an imbalance between protons and neutrons, usually when the ratio of neutrons to protons is too low, the isotope will want to transform itself into a more stable form — a different atom. When this happens, the atom decreases its mass by emitting alpha particles , beta particles , positrons or gamma rays , but some may also gain stability through spontaneous fission or electron capture.
It is a spontaneous process that is known as radioactive decay. Alpha decay: Alpha decay occurs when the atom ejects a particle from the nucleus which consists of two neutrons and two protons, causing the atomic number to decrease by two and the mass to decrease by four. What is radioactive dose? Nuclear Reactor Risk Assessment?
What is a nuclear fuel cycle? Computing the energy density of nuclear fuel Barn Jams! What are Isotopes and Nuclides? Isotopes Elements are your basic chemical building blocks. Figure 1. The Periodic Table of the Elements. Figure 2. Elements have families as well, known as isotopes.
Isotopes are members of a family of an element that all have the same number of protons but different numbers of neutrons. For example, carbon has six protons and is atomic number 6. Carbon occurs naturally in three isotopes: carbon 12, which has 6 neutrons plus 6 protons equals 12 , carbon 13, which has 7 neutrons, and carbon 14, which has 8 neutrons.
Every element has its own number of isotopes. Carbon is stable, meaning it never undergoes radioactive decay.
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