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Nuclei Numerical Practise Reasoning Assertion and Case Study for CBSE Board Exam

Binding Energy Concept in Physics Binding energy refers to the energy required to disassemble a nucleus into its individual protons and neutrons, or equivalently, the energy released when the nucleus is formed from these particles. This energy is a direct measure of the stability of a nucleus. Key Points of Binding Energy: Definition: Binding energy is the energy required to break the nucleus apart into its constituent protons and neutrons. It is also the energy released when a nucleus is formed from free protons and neutrons. Mass-Energy Equivalence: The concept of binding energy is closely related to Einstein’s mass-energy equivalence principle, E=mc^2. When nucleons (protons and neutrons) bind together to form a nucleus, some mass is lost. This mass difference (known as the mass defect) corresponds to the binding energy. Mass defect: The total mass of a nucleus is slightly less than the sum of the masses of its individual protons and neutrons. The missing mass is converted into energy (binding energy) that holds the nucleus together. Formula for Binding Energy: Binding energy=(Mass of nucleons−Mass of nucleus)×c^2 where: c is the speed of light. The mass difference (mass defect) is expressed in atomic mass units (amu) and can be converted to energy using 1 amu=931.5 MeV1amu=931.5MeV. Binding Energy per Nucleon: Binding energy per nucleon is the total binding energy divided by the number of nucleons (protons and neutrons). It gives a measure of the stability of the nucleus. For light elements like hydrogen and helium, the binding energy per nucleon is relatively low. For medium-sized elements like iron and nickel, the binding energy per nucleon reaches a maximum, indicating these nuclei are the most stable. For heavy elements like uranium, the binding energy per nucleon decreases, indicating these nuclei are less stable and can undergo fission. Significance of Binding Energy: Nuclear Stability: The higher the binding energy per nucleon, the more stable the nucleus is. Iron-56 and nickel-62 are among the most stable nuclei, with the highest binding energy per nucleon. Nuclear Reactions: Binding energy plays a crucial role in both nuclear fusion (where light nuclei combine to form a heavier nucleus) and nuclear fission (where heavy nuclei split into lighter nuclei). Both processes release energy because the products have a higher binding energy per nucleon than the reactants. In fusion, the energy is released when lighter nuclei (like hydrogen) combine to form a heavier nucleus (like helium), as the binding energy per nucleon increases. In fission, the energy is released when a heavy nucleus (like uranium-235) splits into lighter nuclei, again because the resulting nuclei have a higher binding energy per nucleon. Example of Iron-56: Iron-56 has one of the highest binding energies per nucleon (~8.8 MeV), making it very stable. As a result, nuclei lighter than iron can release energy by fusion, and nuclei heavier than iron can release energy by fission. Formula for Binding Energy: Binding energy=(Mass of nucleons−Mass of nucleus)×c^2 where: c is the speed of light. The mass difference (mass defect) is expressed in atomic mass units (amu) and can be converted to energy using 1 amu=931.5 MeV1amu=931.5MeV. Binding Energy per Nucleon: Binding energy per nucleon is the total binding energy divided by the number of nucleons (protons and neutrons). It gives a measure of the stability of the nucleus. For light elements like hydrogen and helium, the binding energy per nucleon is relatively low. For medium-sized elements like iron and nickel, the binding energy per nucleon reaches a maximum, indicating these nuclei are the most stable. For heavy elements like uranium, the binding energy per nucleon decreases, indicating these nuclei are less stable and can undergo fission. Significance of Binding Energy: Nuclear Stability: The higher the binding energy per nucleon, the more stable the nucleus is. Iron-56 and nickel-62 are among the most stable nuclei, with the highest binding energy per nucleon. Nuclear Reactions: Binding energy plays a crucial role in both nuclear fusion (where light nuclei combine to form a heavier nucleus) and nuclear fission (where heavy nuclei split into lighter nuclei). Both processes release energy because the products have a higher binding energy per nucleon than the reactants. In fusion, the energy is released when lighter nuclei (like hydrogen) combine to form a heavier nucleus (like helium), as the binding energy per nucleon increases. In fission, the energy is released when a heavy nucleus (like uranium-235) splits into lighter nuclei, again because the resulting nuclei have a higher binding energy per nucleon.