Answer to Question #112384 in Atomic and Nuclear Physics for DEEPAK SINGH

Question

explain the binding energy of the nucleus. show how the concept of binding energy is related to the stability of the atomic curve.

Answer 1

The fact that there is a peak in the binding energy curve in the region of stability near iron means that either the break-up of heavier nuclei (fission) or the combining of lighter nuclei (fusion) will yield nuclei which are more tightly bound (less mass per nucleon).

Importance of Binding energy curve:-

Nuclear binding energy is defined as the energy required to break up a nucleus into its individual; nucleons i.e. protons and neutrons. More important than the total binding energy is the energy per nucleon against mass number.

Mean binding energy is helpful to compare the stability of nuclei of different elements. Except for fluctuations at the lower mass numbers, binding energy increases with A, goes through a maximum at A=60 and then decreases. Hence, nuclei of maximum stability have mass numbers of about 60. The elements with low or high mass numbers become more stable by acquiring mass number of about 60. Because of the maximum in the binding energy per particle that occurs near mass number 60 is a process that releases energy.

Stability of atomic nuclei: the higher the curve, the more stable the nucleus. Assume that the peak is near A=60. These nuclei (which are near iron in periodic table and are called iron peak nuclei) are most stable in the Universe. There are two possibilities suggested by shape of this curve for converting significant amounts of mass into energy.

From the curve of binding energy, heaviest nuclei are less stable than the nuclei near A=60. This suggests that energy can be released if heavy nuclei split apart into smaller nuclei having masses nearer to A=60. This process is called ‘fission’. It is the process that powers atomic bombs and nuclear power reactors.

Fusion reactions: The curve of binding energy indicates a second way in which energy could be released in nuclear reactions. Lightest elements (like hydrogen & helium) have nuclei that are less stable than heavier elements up to A nearly equal to 60. So, sticking two light nuclei together to form a heavier nucleus can release energy. This process is called ‘fusion’ and is the process that powers hydrogen bombs and fusion energy reactors.

In both fusion and fission reactions, total masses after the reaction are less than those before. The ‘missing mass’ appears as energy, with amount given by famous Einstein equation E = mc²

Both fission and fusion reactions have the potential to convert a small amount of mass into a large amount of energy and could account for the energy sources of stars. However, stars are made from light elements. Thus, fission cannot be initiated in stars as a source of energy but fusion is quite possible if right conditions prevail. These conditions can be found in the cores of stars and thermonuclear fusion is the primary source of stellar energy.