Definition of Nuclear Binding Energy:
“Binding energy is the minimum energy compulsory to disassembled or break the nucleus of an atom into its constituent part. This is particularly pertinent to sub-atomic elements in atomic nuclei, to electrons bound to nuclei in atom. “
Facts about Binding Energy:
Binding Energy (BE/A) Curve :
The mass of an atomic nucleus is usually less than the sum of the individual masses of the constituent protons and neutrons and this difference of mass is acknowledged as the mass defect, and signifies the energy that is to be released if a nucleus form.
Binding Energy Formula :
The binding energy for a nucleus is given by the equation
Patterns in the binding energy per nucleon, BE/A. if the BE/A is higher, the more stability of the nucleus will become higher too.
Critical Energy :
The minimum excitation energy required for fission to occur is known as the critical energy (EC) or threshold energy.
In principle, a nucleus, if energize sufficiently high excited state, can be parted into constituent parts. For ideal fission condition, the excitation energy must be more than a specific value for that nuclide. The min excitation energy requires for fission to occur is identified as the critical energy (E critical) or threshold energy. This critical energy be subject to nuclear structures also as it is dependent on various nucleus characteristics. This value may be significantly higher for light nuclei with Z < 90. For heavier nuclei with Z > 90, this may in the range of 4 to 6 MeV for A-even nuclei, and this value is considerably lesser for A-odd nuclei
Negative Binding Energy per Nucleon Curve
The negative of binding energy per nucleon for stable isotopes along the valley of stability.
The dissociation energy Ed is equivalent to the diff. in-between the binding energy of the compound nucleus going thru fission and the sum of the binding energy of the fission fragments. The min activation energy Ea that has to be supplementary to a nucleus to go thru fission reaction is therefore Ec – Ed.
Mass of a Neutron ; Mass of a Proton and Mass of an electron in kg and amu
Nuclear mass and unit conversion in kg, amu and energy
Atomic mass unit (amu)
Atomic mass unit: Abbreviated as “amu.” A mass equal to one twelfth the mass of an atom of carbon-12.
amu to kg
1 amu = 1.66053873 x 10 -27 kilogram
1 amu= 1.66053873 x 10 -24 gram.
Table of critical energies and binding energies of radioactive fuels:
This is generally found for heavy elements; A radioactive decay occurs. The nuclear binding energy of the elements reaches its maximum; spontaneous breakdown into lesser mass nucleus and some isolated particle with more atomic mass numbers might also generate.
The nuclear binding energy is maximum for an atomic mass number of 56
Spontaneous fission half-life of various nuclides in reliant on their Z2/A ratio. In above figure Nuclides of the same element are linked with a red line. The green line illustrates the upper limit of half-life.
Valley of Stability Parabola
Semi empirical mass formula discrepancy
The discrepancy between experimentally-obtained binding energies and those predicted by the SEMF, alongside nuclear shell lines.
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