# Why Is Nuclear Binding Energy Proportional to the Mass Defect?

• semc
In summary, the binding energy of a nucleus is directly proportional to the difference between the total mass before and after the combination. This is due to the transformation of energy, often resulting in a gamma ray, when comparing a nucleus of mass M+1 to the initial nucleus of mass M and the mass of a proton or neutron.
semc
lets say the nucleus of the nuclide is M, why is binding energy of the nucleus directly proportional to (mass of proton and neutron)-M ? shldnt it be M-(mass of proton and neutron) ?

Last edited:
Binding energy is the difference between the total mass (before) and the total mass (after) the combination.

If one takes a nucleus of mass M+1 and compares it to the initial nuclear of mass M and the proton or neutron mass, one will find the total mass before is greater than the mass after. The difference in mass is the binding energy, and in many cases the energy is transformed into a gamma ray.

http://hyperphysics.phy-astr.gsu.edu/Hbase/nucene/nucbin.html

The binding energy of a nucleus is a measure of the energy required to break apart the nucleus into its individual protons and neutrons. This energy is directly related to the mass of the nucleus, which is composed of protons and neutrons.

The equation E=mc^2 tells us that energy and mass are equivalent, and that the mass of a system is related to its energy content. In the case of a nucleus, the mass of the nucleus is slightly less than the combined mass of its individual protons and neutrons. This difference in mass is known as the mass defect and is due to the strong nuclear force that binds the protons and neutrons together.

Therefore, the binding energy of a nucleus is proportional to the mass defect, which is the difference between the mass of the nucleus and the mass of its individual protons and neutrons. This is why the binding energy is directly proportional to the sum of the masses of the protons and neutrons, rather than the difference.

In summary, the binding energy of a nucleus is directly proportional to the mass of its constituent particles, taking into account the mass defect caused by the strong nuclear force.

## 1. What is nuclear physics?

Nuclear physics is a branch of physics that studies the properties and behavior of atomic nuclei, as well as the particles and energy that interact with them.

## 2. What are the main applications of nuclear physics?

Nuclear physics has various applications in fields such as energy production, medicine, and nuclear weapons. It is also used in scientific research to study the fundamental nature of matter and the universe.

## 3. What is nuclear fission and fusion?

Nuclear fission is the process of splitting a heavy nucleus into smaller nuclei, releasing a large amount of energy. Nuclear fusion is the process of combining two lighter nuclei into a heavier nucleus, also releasing a large amount of energy.

## 4. What are the risks associated with nuclear energy?

The main risks associated with nuclear energy include the potential for accidents at nuclear power plants, the production of radioactive waste, and the potential for nuclear weapons proliferation.

## 5. How do scientists study nuclear physics?

Scientists study nuclear physics through experiments using particle accelerators and nuclear reactors, as well as through theoretical modeling and computer simulations. They also use data from natural sources, such as cosmic rays and radioactive elements in the Earth's crust.

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