Mass-Energy and Nuclear Binding Energy

The energy-mass relationship in physics is the relationship between mass and energy in the rest frame of a system, where the only difference between the two values is a constant and the unit of measurement. The famous formula of physicist Albert Einstein describes this principle. The energy necessary to completely divide an atomic nucleus into its constituent protons and neutrons, or, equivalently, the energy liberated by merging individual protons and neutrons into a single nucleus, is known as nuclear binding energy. 

Nuclear binding energy is the minimum energy required to disintegrate an atom’s nucleus into its constituent protons and neutrons, collectively known as nucleons. The binding energy for stable nuclei is always positive as the nucleus needs to gain energy to facilitate the nucleons to move apart from each other. 

Nuclear binding energy is a negative quantity in theoretical nuclear physics. When the constituent nucleons are infinitely far apart, it indicates the energy of the nucleus relative to the energy of the constituent nucleons. The mass of an atom is always slightly less than the total of the masses of the individual neutrons, protons, and electrons that make up the atom, according to careful measurements. The mass defect (m) is the discrepancy between the mass of an atom and the sum of its components’ masses.

What is Mass Defect? 

The discrepancy between an atom’s mass and the sum of its protons, neutrons, and electrons is known as a mass defect. Since, some of the mass is released as energy when protons and neutrons bond in the atomic nucleus, the real mass differs from the masses of the components. A helium atom with two protons and two neutrons (four nucleons), for example, has a mass around 0.8 percent lower than four hydrogen nuclei, each of which has one nucleon.

What is Nuclear Binding Energy? 

It is the energy crucial to entirely divide an atomic nucleus into its subsequent particles: protons and neutrons. Thus, the energy that is disentangled by integrating individual protons and neutrons into a single nucleus is recognised as nuclear binding energy. 

If we give 2.23 million eV of energy to the nucleus of a hydrogen-2 atom, it is bound to divide into its counterparts. It splits into a proton and a neutron. When this phenomenon occurs, the emission of gamma radiation can be observed. 

Conservation of Mass and Energy:

The conservation of energy, like the conservation of momentum, is a universal principle in physics that applies to all interactions. In some relativistic conditions, however, the classical conservation of mass is compromised. The conversion of mass into kinetic energy in nuclear processes and other interactions between elementary particles have all been experimentally confirmed to support this theory. While current physics has abandoned the term “mass conservation”, a relativistic mass can be described as the energy of a moving system, allowing for relativistic mass conservation. When the energy associated with a particle’s mass is changed into other forms of energy, such as kinetic energy, thermal energy, or electromagnetic energy, mass conservation is broken.

Combining Nuclei:

Smaller nuclei can join to form larger nuclei and produce energy, but the quantity of energy released is significantly lower than in hydrogen fusion. The reason for this is that, while the whole process releases energy by allowing nuclear attraction to function, energy must first be input to drive positively charged protons together, which repel each other due to their electric charge.

Binding Energy per nucleon:

• In the sequence from magnesium to xenon, a region of rising binding energy is followed by an area of relative saturation. As the atomic mass increases, attractive nuclear forces in this area are roughly corresponded by repulsive electromagnetic forces amidst the protons as the atomic number increases.
• When we move from magnesium to xenon, there is a region of rising nuclear binding energy. This region subsequently has the relative saturation region. The nucleus has grown large enough in this region that nuclear forces can no longer fully reach throughout its width.
• As the atomic number of atoms heavier than xenon grows, the binding energy per nucleon decreases. The strong nuclear forces are overpowered by the strong repulsive electromagnetic forces. 
• Nickel-62 is the greatly bonded nucleus at the peak of binding energy. It is followed by iron-58 and iron-56. 

Conclusion: 

The terms energy and mass are interchangeable. Nuclear binding energy is the amount of energy necessary to divide an atom’s nucleus into its constituent parts. Nuclear binding energy is used to assess whether fission or fusion is the better option. The difference between the mass of a nucleus and the sum of the masses of the nucleons that make it up is the mass defect of a nucleus, which represents the mass of the energy binding the nucleus. A mass defect is a difference between an atom’s mass and the sum of its protons, neutrons, and electrons.