What is meant by binding energy per nucleon?
Condradiction in theoratical and experimental values signifies an error usually..but an exeption when the mass of nucleus is calculated by theory say suming up the mas of protons and neutrons while the other way is experemental say by spectroscopy.The values were not same.this condradiction actually given rise to a nee term binding energy.Binding energy is the energy that holds up the nucleus as it is…so whats the role of mass defect here.let me explain by einsteins theory of relativity E=mc^2.the experemental mass of nucleus where less than the theoratical value that mass is been converted to energy by the above equation.binding energy per nucleon is the energy required to desassemble the nucleus of an atom to its component parts.
What has the highest binding energy per nucleon, Fe56 or Ni62?
Nuclear Binding Energy CurveThe binding energy curve is obtained by dividing the total nuclear binding energy by the number of nucleons. The fact that there is a peak in the binding energy curve in the region of stability near iron means that either the breakup of heavier nuclei (fission) or the combining of lighter nuclei (fusion) will yield nuclei which are more tightly bound (less mass per nucleon).The binding energies of nucleons are in the range of millions of electron volts compared to tens of eV for atomic electrons. Whereas an atomic transition might emit a photon in the range of a few electron volts, perhaps in the visible light region, nuclear transitions can emit gamma-rays with quantum energies in the MeV range.The iron limitThe buildup of heavier elements in the nuclear fusion processes in stars is limited to elements below iron, since the fusion of iron would subtract energy rather than provide it. Iron-56 is abundant in stellar processes, and with a binding energy per nucleon of 8.8 MeV, it is the third most tightly bound of the nuclides. Its average binding energy per nucleon is exceeded only by 58Fe and Ni62, nickel isotope being the most tightly bound nuclides. Hence Ni62 has more binding energy per nucleon
How does binding energy per nucleon affect the stability of the nucleus?
It is found that the mass of a nucleus is always less than the sum of masses of the nucleons constituting it. It meas certain mass disappears when a number of nucleons are brought together to form a nucleus. This difference between the sum of the rest masses of nucleons constituting the nucleus and the rest mass of nucleus itself is called mass defect of the nucleus.This mass defect is converted into energy by Einstein’s mass energy relationship which is called binding energy that helds the nucleons together, so more is the mass defect more will be the binding energy and more it will be stable.But the more important term is binding energy per nucleon which is the energy required to remove one nucleon from it’s parent nucleus.The Binding Energy Graph shows the variation of binding energy per nucleon with increase in mass no.Light and Heavy Nuclei have lesser binding energy per nucleon as compared to the mid range nuclei.Initially binding energy per nucleon is small(for light nuclei) then increases and attains a maximum value for iron(mid range nuclei) and then again decreases(for heavy nuclei)That’s why mid range nuclei are more stableThe formula for Binding Energy is derived in the video link below#FOR M0RE DETAILS ABOUT BINDING ENERGY CURVE WATCH THE VIDEO LINK GIVEN BELOWPACKING FRACTIONThe deviation of the masses of nuclei and its constituents particles i.e nucleons is expressed in terms of a parameter PACKING FRACTIONf = (M-A)/AA= Mass no.(Theoretical/Expected Mass) , M= Atomic mass(Measured/Experimental mass)Packing Fraction measures the stablity of the nucleus. Smaller the value of f higher is the stablity of the nucleus.Explanation:-For light nuclei M>A so f is positive so nucleus is unstable. This is because in this case Sum of masses of constituent nucleons(A) is smaller than the mass of nucleus(M), that is mass defect is small so is the binding energyFor mid range nuclei MA so f is positive again and that’s why nucleus becomes unstableMORE IS THE MASS DEFECT ,MORE NEGATIVE IS THE PACKING FRACTION AND HIGHER IS THE BINDING ENERGY PER NUCLEON AND MORE STABLE IS THE NUCLEUS THAT’S WHY THEIR GRAPHS ARE OPPOSITE.# FOR MORE DETAILS ABOUT BINDING ENERGY, PACKING FRACTION AND THEIR CURVES WATCH THE VIDEO LINK BELOW.
Why is binding energy per nucleon doesn't vary much for elements with 30 Ah, my favorite topic. Clearly we do not understand something. The “binding energy,” of course, is hypothetical. What we do know is that atomic nuclei weigh less than a collection of protons and neutrons in the same numbers (as dictated by charge and approximate mass). It is because mass is quantized that the nuclei cannot separate into these separate particles because there isn’t enough mass to make them. So, in essence you now have a single particle with a large positive charge. The binding energy is calculated as the amount of energy needed to separate the nucleus into those particles and represents the E=mc(2) based upon the missing mass but it is interpreted (by too many) as the source of some mysterious force holding the separate protons and neutrons together. This is unwarranted.I would like to know what component particles of nucleons (undiscovered quarks?) which are sacrificed to make these nuclei. It there is not such particles, then the masses of protons and neutrons are variable (highly so because the binding energy does vary per nucleon for the various nuclei) which will require quite some explaining.
During the formation of a nucleus, protons and neutrons both take part. Which one has more contribution in binding energy by contributing its mass to energy?
The protons in a nucleus inherently want to repel each other in that sense the are very much a coiled spring and that coiled spring stores a lot of potential energy. The binding energy/ force provided by the strong nuclear force is mediated via the neutrons. Hence atoms are only stable when there is approximately 1 neutron for each proton. Hydrogen only has one proton and so needs no neutron. Neutrons feel no repulsive force and so do not store any of the potential energy of binding. So if the question is which nucleon’s (proton or neutron) mass is distorted within the nucleus and stores the binding energy, it is the proton. There is much more to be said on the subject. For example, why does the binding energy per nucleon vary as it does across the periodic table etc.
Why is the binding energy per nucleon greater for intermediate nuclei?
For small or light nuclei, a nucleon has only few compatriots to bind with, so average binding is weak.For heavy or massive nuclei, the positively charged nucelons (protons) on opposite sides of the nucleus are repelling each by electrostatic repulsion, and the strong nuclear force is very weak at these distances. So average binding is weak.Only for medium sized nuclei is each nucleon fully within range of all its fellow nucleons' strong force, and there are a lot of them. So average binding is strong for these nuclei.
How do you calculate the binding energy per nucleon?
Consider a nucleus [math]{^A_ZX}[/math]. [math]A[/math] is the number of nucleons (mass number) and [math]Z[/math] is the number of protons (Atomic number).Mass defect, [math]\Delta M = {Z m_P + (A - Z)m_n - m({^A_ZX})}[/math]Binding energy, [math]E_b = \Delta Mc^2 = [{Z m_P + (A - Z)m_n - m({^A_ZX})}]c^2[/math]Binding energy per nucleon, [math]E_{bn} = \frac{E_b}{A}[/math]
Why does nuclear fusion release more energy than nuclear fission?
Heavy elements (e.g., uranium) have 92 protons tied together in one nucleus by the short-range nuclear strong force and repelled by the Coulombic force. If the nucleus splits, the attractive force is only slightly reduced (because the nucleons only attract close nucleons strongly), but the longer-range repulsive force is cut dramatically. The average binding force for the 235–238 nucleons of uranium is about 7.7 MeV; after the split (e.g., into iron, tho it’s more complex), the average binding force per nucleon increases to about 8.8 MeV. Thus, one uranium fission can yield 260 MeV of energy.Deuterium (one proton, one neutron) is bound with an energy of 2.4 MeV, or 1.2 MeV per nucleon. When two deuteriums fuse, helium is produced with a binding energy of 28 MeV. The gain is 23.2 MeV. One fusion produces 9% of the energy of one fission. But we should compare equal starting masses: one fission (~235 nucleons) vs 59 fusions of 4 nucleons each. The comparison is then 260 MeV vs 1363 MeV.The binding energies of the elements rise to a maximum stability at iron, then decrease. The heavy elements are produced in supernovas and “cooled” down before they can equilibrate to form iron. We got some of that star dust on earth. Wikipedia has a good article. Here is a chart of the binding energies.