19.4
Nuclear Binding Energy
The difference between the calculated and experimentally measured masses is known as the mass defect of the atom. In the case of helium-4, the mass de…
Nuclear stability is best quantified in terms of nuclear binding energy.
Consider the helium-4 atom, which has two each of protons, neutrons, and electrons. The sum of the known masses of these particles is greater than the measured mass of neutral helium-4 by 0.0305 atomic mass units.
The difference between the calculated and experimentally measured atomic masses is called the mass defect. The large amount of energy released during the formation of helium-4 is the reason for this difference.
Einstein’s mass–energy equivalence helps to estimate the energy change associated with the loss in mass. Converting the mass to kilograms and solving the equation results in the base SI units for joules. It is evident that an enormous amount of energy accompanies the tiny change in mass.
The energy released when the nucleons bind together is the same as the energy required to break that nucleus into its constituent protons and neutrons and is called nuclear binding energy. For helium, this is 2.74 terajoules per mole.
Dividing by Avogadro's number gives 4.55 picojoules for the nuclear binding energy per helium nucleus. This is often expressed in electronvolts as well. For helium-4, this turns out to be 28.4 megaelectronvolts per nucleus. When divided by the number of nucleons, 4, this yields the nuclear binding energy per nucleon.
The plot of nuclear binding energy per nucleon versus mass number depicts the comparative stabilities of the nuclides. The elements with mass numbers ranging from 40 to 100 have the highest per-nucleon binding energy, and iron-56 has the lowest mass per nucleon.
To attain stability, heavy nuclei tend to fragment to midsize nuclei through an exothermic process called fission, whereas lighter nuclei combine through the fusion process
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Q1: What is mass defect and why does it occur in atoms?
Mass defect is the difference between the calculated sum of individual particle masses and the experimentally measured atomic mass. In helium-4, this difference is 0.0305 atomic mass units. The mass defect occurs because mass converts to energy during nucleus formation, as described by Einstein's mass-energy equivalence equation E = mc².
Q2: How is nuclear binding energy calculated from mass defect?
Nuclear binding energy is calculated by converting the mass defect to kilograms and applying Einstein's equation E = mc², where c is the speed of light. For helium-4, the mass defect of 0.0305 grams per mole converts to 3.05 × 10⁻⁵ kilograms per mole, yielding a binding energy of 2.74 terajoules per mole.
Q3: What does binding energy per nucleon tell us about nuclear stability?
Binding energy per nucleon measures the average energy holding each nucleon in the nucleus and indicates relative nuclear stability. Elements with mass numbers between 40 and 100 have the highest binding energy per nucleon, with iron-56 being most stable. Higher binding energy per nucleon correlates with greater nuclear stability.
Q4: Why are electronvolts commonly used to express nuclear binding energy?
Electronvolts (eV) are convenient units for nuclear binding energy because they represent the energy scale of nuclear processes. One electronvolt equals 1.602 × 10⁻¹⁹ joules. Helium-4's binding energy of 28.4 megaelectronvolts per nucleus is more practical to express in eV than in joules.
Q5: How do heavy and light nuclei achieve stability differently?
Heavy nuclei achieve stability through nuclear fission, fragmenting into midsize nuclei in an exothermic process. Lighter nuclei achieve stability through nuclear fusion, combining to form larger nuclei. Both processes release energy because midsize nuclei have the highest binding energy per nucleon.
Q6: What is the relationship between mass and energy in nuclear reactions?
Nuclear reactions convert mass directly into energy through Einstein's mass-energy equivalence, E = mc². The energy changes in nuclear reactions are vastly greater than in chemical reactions because even tiny mass changes produce enormous energy. This principle explains why nuclear binding energy is so substantial compared to chemical bond energies.
Q7: How do you convert binding energy from molar to per-nucleus values?
Binding energy per nucleus is calculated by dividing the molar binding energy by Avogadro's number (6.022 × 10²³). For helium-4, the molar binding energy of 2.74 terajoules per mole divided by Avogadro's number yields 4.55 picojoules per nucleus, or 28.4 megaelectronvolts per nucleus.