# Mass defect and binding energy help

• |mathematix|
In summary: This process also releases energy, as the resulting nucleus is in a more tightly bound state than the initial protons. The energy released in this process is ultimately due to the nuclear strong force, which is responsible for binding nucleons together in a nucleus. The increase in binding energy per nucleon during fusion reactions is what causes the liberation of energy. Similarly, in fission reactions, the decrease in binding energy per nucleon is what leads to the release of energy.In summary, nuclear force always exists between nucleons in a nucleus and is responsible for binding them together. The energy required to break down a nucleus is called nuclear binding energy, and the mass defect is a measure of this energy.
|mathematix|
I don't know if I completely understand mass defect and binding energy so I will write what I understand and hopefully you can explain any misunderstandings I have.

I know what mass defect is and that I understand that we need the strong nuclear force to keep the nucleus together etc. but I don't understand where binding energy comes from.

So if we have a proton and a neutron and we bring them together to form a deuterium atom, will some of the mass of each become converted into strong nuclear force to keep them together? Where does the energy liberated come from then? Shouldn't there be energy liberated when two nuclei are fused together? Also, can you explain the effect of gravitational potential energy? Is the decrease in GPE the reason why energy is liberated?

So basically, where does the energy of mass defect go (becomes strong force?) and where does the energy of fusion reactions come from?

If we want to separate a nucleus into its constituents, we have to provide energy equivalent to mass defect, correct? According to E=mc^2, the energy put into the system to separate nucleons is transformed into mass, making the final particles heavier (their actual mass). This creates and is equivalent to the mass defect.

Or does nuclear energy come from either splitting high-mass nuclei or fusing lighter nuclei as this increases the binding energy per nucleon?

Thank you!

connorp
You cannot "convert a mass into a force". The nucleons attract each other, if they merge they release energy, the total energy (in the rest frame) of the system reduces, therefore the mass reduces.
Shouldn't there be energy liberated when two nuclei are fused together?
It is.
Also, can you explain the effect of gravitational potential energy? Is the decrease in GPE the reason why energy is liberated?
You can have the same effect with gravity (collapsing stars, ...). For nuclei, gravity is irrelevant, however.
If we want to separate a nucleus into its constituents, we have to provide energy equivalent to mass defect, correct?
Right
Or does nuclear energy come from either splitting high-mass nuclei or fusing lighter nuclei as this increases the binding energy per nucleon?
Those are methods to release energy (by producing nuclei with more binding energy).

mfb said:
Those are methods to release energy (by producing nuclei with more binding energy).

So nuclear force always exists between any two nucleons and when nucleons come together to create a nucleus, mass defect provides the binding energy, so nuclear force has nothing to do with energy released in nuclear reactions (bombs, etc.). Increasing binding energy causes the liberation of energy in nuclear reactions.

Thank you!

So nuclear force always exists between any two nucleons
Its range is very short.
so nuclear force has nothing to do with energy released in nuclear reactions (bombs, etc.)
How did you get that impression? The strong force is the (main) cause for nuclear binding energies, and nuclear bombs just release energy based on the binding energy differences of different nuclei.

mfb said:
Its range is very short.
How did you get that impression? The strong force is the (main) cause for nuclear binding energies, and nuclear bombs just release energy based on the binding energy differences of different nuclei.

I didn't use the right words to say what I mean :( I meant to say that when the binding energy per nucleon is increases, energy is liberated (which is ultimately due to nuclear strong force).

Right.

|mathematix| said:
So nuclear force always exists between any two nucleons and when nucleons come together to create a nucleus, mass defect provides the binding energy, so nuclear force has nothing to do with energy released in nuclear reactions (bombs, etc.). Increasing binding energy causes the liberation of energy in nuclear reactions.

Thank you!
This is a bit confusing. But nuclear force always exists among nucleons in a nucleus.

The energy required to break down a nucleus into its component nucleons is called the nuclear binding energy.
http://www.chem.purdue.edu/gchelp/howtosolveit/Nuclear/nuclear_binding_energy.htm#Top

The mass defect is merely a measure of the binding energy required to remove a nucleon, or nucleons from a nucleus, or if enough energy could be applied, to dissociate a nucleus into it's constituent components. The mass defect is a manifestation of the nucleons settling into a lower energy state, somewhat analogous to atoms forming molecules.

The binding energy may be expressed in the form of a gamma ray, or kinetic energy of nuclei, which is the case with most fusion reactions or all fission reactions. In fission, the two nuclei (fission products) are in a tighter bound state (greater binding energy per nucleon) that the nucleus that fissioned. Note that 2 or 3 neutrons are also released in the fission process, as are gamma rays in some cases.

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

Deuterons can be formed by a proton and neutron combining, in which case a gamma ray is emitted with an energy equivalent to the binding energy, or by pp fusion, in which a positron and neutrino are emitted.
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/procyc.html#c4

Astronuc said:
This is a bit confusing. But nuclear force always exists among nucleons in a nucleus.

The energy required to break down a nucleus into its component nucleons is called the nuclear binding energy.
http://www.chem.purdue.edu/gchelp/howtosolveit/Nuclear/nuclear_binding_energy.htm#Top

The mass defect is merely a measure of the binding energy required to remove a nucleon, or nucleons from a nucleus, or if enough energy could be applied, to dissociate a nucleus into it's constituent components. The mass defect is a manifestation of the nucleons settling into a lower energy state, somewhat analogous to atoms forming molecules.

The binding energy may be expressed in the form of a gamma ray, or kinetic energy of nuclei, which is the case with most fusion reactions or all fission reactions. In fission, the two nuclei (fission products) are in a tighter bound state (greater binding energy per nucleon) that the nucleus that fissioned. Note that 2 or 3 neutrons are also released in the fission process, as are gamma rays in some cases.

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

Deuterons can be formed by a proton and neutron combining, in which case a gamma ray is emitted with an energy equivalent to the binding energy, or by pp fusion, in which a positron and neutrino are emitted.
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/procyc.html#c4

Thank you! I think I understand all of it except the last part :(

"Deuterons can be formed by a proton and neutron combining, in which case a gamma ray is emitted" why are gamma rays emitted? Does this have to do with the nucleons going to a 'lower energy state' and thus releasing energy?

|mathematix| said:
Thank you! I think I understand all of it except the last part :(

"Deuterons can be formed by a proton and neutron combining, in which case a gamma ray is emitted" why are gamma rays emitted? Does this have to do with the nucleons going to a 'lower energy state' and thus releasing energy?
Neutron capture by a nucleus is usually associated with gamma emission. The reaction is referred to as (n,γ). When a nucleus absorbs a neutron, it changes the nuclear configuration (A -> A+1), and the mass of nucleus is less than the mass of the initial nucleus and free neutron.

Bascially it has to do with the nucleons forming a more bounded state as compared to the free nucleons.

Upon neutron absorption, some nuclei form metastable states, which decay by isomeric transition, i.e., gamma emission. This is related to nucleon spin.
http://epubs.surrey.ac.uk/469/1/fulltext.pdf

I was under the impression that when a particle passes the Coulomb barrier, it releases it's binding energy and enters the nucleus. The mass defect is the summation of the released binding energies of the nucleons in an atom. For instance the mass defect is the difference in mass between an isotope and the sum of the mass of the nucleons in the atom. Is that right?

## 1. What is mass defect and how is it related to binding energy?

Mass defect is the difference between the mass of an atom's nucleus and the sum of the masses of its individual protons and neutrons. This difference is a result of the conversion of some mass into energy, known as binding energy, during the formation of the nucleus. The greater the binding energy, the lower the mass defect and the more stable the nucleus.

## 2. How is mass defect and binding energy calculated?

Mass defect is calculated by subtracting the mass of the individual protons and neutrons from the mass of the nucleus. Binding energy is calculated using Einstein's famous equation, E=mc^2, where E is the energy, m is the mass defect, and c is the speed of light. This equation shows the relationship between mass and energy, and how they are interchangeable.

## 3. What is the significance of mass defect and binding energy in nuclear reactions?

Mass defect and binding energy play a crucial role in nuclear reactions, particularly in nuclear fusion and fission. In fusion reactions, the combining of two nuclei releases a large amount of binding energy, resulting in a decrease in mass and the release of energy. In fission reactions, the splitting of a heavy nucleus also releases binding energy. Understanding these concepts is essential in harnessing nuclear energy for various applications.

## 4. How are mass defect and binding energy related to the stability of an atom?

As mentioned earlier, the greater the binding energy, the lower the mass defect and the more stable the nucleus. This is because the released binding energy is used to hold the nucleus together, counteracting the repulsive forces between positively charged protons. The more stable an atom's nucleus, the less likely it is to undergo radioactive decay.

## 5. Can mass defect and binding energy be measured experimentally?

Yes, mass defect and binding energy can be measured experimentally using mass spectrometry. This technique allows scientists to measure the masses of individual atoms and determine their mass defects. Additionally, the energy released during a nuclear reaction can also be measured, providing further evidence for the existence and calculation of binding energy.

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