As total number of nucleons in nucleus is equal to mass number. And is also called atomic mass number. I want to know that is there any difference between the two? Because in nuclear reactions mass number differs from atomic mass and the difference between two provides binding energy.
[Physics] the difference between atomic mass and mass number
binding-energydefinitionmassnuclear-physics
Related Solutions
To understand binding energy and mass defects in nuclei, it helps to understand where the mass of the proton comes from.
The news about the recent Higgs discovery emphasizes that the Higgs mechanism gives mass to elementary particles. This is true for electrons and for quarks which are elementary particles (as far as we now know), but it is not true for protons or neutrons or for nuclei. For example, a proton has a mass of approximately $938 \frac{\mathrm{MeV}}{c^2}$, of which the rest mass of its three valence quarks only contributes about $11\frac{\mathrm{MeV}}{c^2}$; much of the remainder can be attributed to the gluons' quantum chromodynamics binding energy. (The gluons themselves have zero rest mass.) So most of the "energy" from the rest mass energy of the universe is actually binding energy of the quarks inside nucleons.
When nucleons bind together to create nuclei it is the "leakage" of this quark/gluon binding energy between the nucleons that determines the overall binding energy of the nucleus. As you state, the electrical repulsion between the protons will tend to decrease this binding energy.
So, I don't think that it is possible to come up with a simple geometrical model to explain the binding energy of nuclei the way you are attempting with your $\left(1\right)$ through $\left(15\right)$ rules. For example, your rules do not account for the varying ratios of neutrons to protons in atomic nuclei. It is possible to have the same total number of nucleons as $\sideset{^{56}}{}{\text{Fe}}$ and the binding energies will be quite different the further you move away from $\sideset{^{56}}{}{\text{Fe}}$ and the more unstable the isotope will be.
To really understand the binding energy of nuclei it would be necessary to fully solve the many body quantum mechanical nucleus problem. This cannot be done exactly but it can be approached through many approximate and numerical calculations. In the 1930's, Bohr did come up with the Liquid Drop model that can give approximations to the binding energy of nuclei, but it does fail to account for the binding energies at the magic numbers where quantum mechanical filled shells make a significant difference. However, the simple model you are talking about will be incapable of making meaningful predictions.
EDIT: The original poster clarified that the sign of the binding energy seems to be confusing. Hopefully this picture will help:
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This graph shows how the potential energy of the neutron and proton that makes up a deuterium nucleus varies as the distance between the neutron and proton changes. The zero value on the vertical axis represents the potential energy when the neutron and proton are far from each other. So when the neutron and proton are bound in a deuteron, the average potential energy will be negative which is why the binding energy per nucleon is a negative number - that is we can get fusion energy by taking the separate neutron and proton and combining them into a deuteron. Note that the binding energy per nucleon of deuterium is $-1.1 \, \mathrm{MeV}$ and how that fits comfortably in the dip of this potential energy curve.
The statement that $\sideset{^{56}}{}{\text{Fe}}$ has the highest binding energy per nucleon means that lighter nuclei fusing towards $\text{Fe}$ will generate energy and heavier elements fissioning towards $\text{Fe}$ will generate energy because the $\text{Fe}$ ground state has the most negative binding energy per nucleon. Hope that makes it clear(er).
By the way, this image is from a very helpful article which should also be helpful for understanding this issue.
Every day observations work with classical physics. If you have 1 gold coin with a mass m, 100 gold coins will have a mass 100m. All the economies of humanity work on the conservations of mass, from wheat production to oil wells mass does not change, is additive and is conserved.
Nuclear reactions were a surprise and are no longer in the framework of classical physics. One needs quantum mechanics and special relativity to really understand what is going on.
Chemists by the year 1789 , long before any special relativity and quantum mechanics appeared, discovered that they could organize the chemical elements . The periodic table of elements shows the A number , which is the atomic weight of the element, i.e. the atomic weight divided by the mass of hydrogen, and Z, the number of positive charges equal to the electron number in the nucleus. They found out that there was a binding energy per nucleon
At the nuclear level, nuclear binding energy is the energy required to disassemble a nucleus into the free, unbound neutrons and protons it is composed of. It is the energy equivalent of the mass excess, the difference between the mass number of a nucleus and its true measured mass.Nuclear binding energy derives from the nuclear force or residual strong force, which is mediated by three types of mesons.
This makes sense only within the context of special relativity, where mass is not a conserved quantity.
You ask:
I mean mass of (what) is converted into energy. Please explain.
An example for fusion: Deuterium and Tritium will release the difference in the binding energies of the end products into the kinetic energy of the end products.
Deuterium + Tritium → Helium + neutron + 340,000,000,000 Joules per gram
The masses of (deuterium+ tritium) will be larger than the mass of Helium +neutron, because mass is not a conserved quantity at this level, it is connected directly with energy according to the special relativity equations .
Best Answer
The mass number is the number of nucleons (protons and neutrons) in the nucleus of an atom.
For example $^{12}_{\,\,6}\rm C$ has a mass number of $12$ as it has $6$ protons and $6$ neutrons in its nucleus and $^{35}_{17}\rm Cl$ has a mass number of $35$ as it has $17$ protons and $18$ neutrons in its nucleus.
The atomic mass of an atom is the mass of the atom in atomic mass units (amu or u).
The atomic mass of a $^{12}_{\,\,6}\rm C$ atom is defined as being $12 $ atomic mass units.
The atomic mass of a $^{35}_{17}\rm Cl$ atom is $34.96885268$ atomic mass units ie a $^{35}_{17}\rm Cl$ atom is $\dfrac{34.96885268}{12}$ heavier than a $^{12}_{\,\,6}\rm C$ atom.
Note that the atomic mass is approximately equal to the mass number.
There is a third quantity which you should be aware of which is used by Chemists and that is the (standard) atomic weight.
The unit is again the atomic mass unit but it is the average atomic mass of the different types of atoms (isotppes) of which an element is composed.
For example in nature carbon exists as the isotopes $^{12}_{\,\,6}\rm C, \, ^{13}_{\,\,6}\rm C$ and $^{14}_{\,\,6}\rm C$ and so you will see the atomic weight of carbon listed as $12.011$ to reflect the fact that natural carbon is $75\%\,^{12}_{\,\,6}\rm C,\, 24\%\,^{13}_{\,\,6}\rm C$ with a trace of $^{14}_{\,\,6}\rm C$.
However the isotopic composition of Carbon may vary and so you will also see the standard atomic weight listed as a range of values such as $[12.0096 \,\,\,12.0116]$ when greater accuracy is required.