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NUCLEAR MASS AND STABILITY (STABLE ISOTOPES (Patterns of nuclear stability…
NUCLEAR MASS AND STABILITY
BINDING ENERGY
The energy liberated in the formation of a nucleus from its component nucleons is a measure of the stability of that nucleus.
Nuclear binding energy (Eb) is the energy that would be required to disassemble the nucleus of an atom into its component parts (neutron and proton)
The EBIA values increase with increasing mass number up to a maximum around mass number 60 and then decrease.
The larger the heat of formation the more stable the molecular since the more energy is required to decompose the molecule into its component atoms.
A better indication of the relative stability of nuclei is obtained when the binding energy is divided by the total number of nucleons to give the binding energy per nucleon, EB/A.
STABLE ISOTOPES
60% of them have both an even number of protons and an even number of neutrons (even-even nuclei).
20% have an even number of protons and an odd number of neutrons (even-odd nuclei).
20% have an odd number of protons and an even number of neutrons (odd-even nuclei).
The pattern of stability is explained in terms of the energy stabilization gained by combination of like nucleons to form pairs-protons with protons and neutrons with neutrons.
Elements of even atomic number (i.e. even number of protons) are characterized by having a relatively sizable number of stable isotopes, usually 3 or more.
Patterns of nuclear stability
If the neutron number is uneven, there is still some stability conferred through the proton-proton pairing.
For elements of odd atomic number, unless there is stability due to a even neutron number (neutron-neutron pairing), the nuclei are radioactive with rare exeptions.
ATOMIC MASS
Mass ma of an atom with mass number A would be given by the number of protons (Z) x the mass of the hydrogen atom (MH) + the number of neutrons (N) x the mass of the neutrons (Mn).
Mass defect
This actually represents the energy that was released when the nucleus was formed (binding energy).
Mass defect is the 'missing mass' as the mass of an atomic nucleus is less than the sum of individual protons and neutrons.
Characteristics of nucleus
Total energy of the nucleus is directly proportional to the total number of nucleons.
Binding energy is reduced by a term which allows for variation in the ratio of the number of protons and neutrons.
Odd-even effect.
Negative term reflecting the repulsive forces of the protons.
Effect of surface tension.
COULOMB FORCE
The magnitude of the electric force that a particle exerts on another particle is directly proportional to the product of their charges and inversely proportional to the square ot he distance between them.
NEUTRON TO PROTON RATIO
Same ratio
In the light elements, stability is achieved when the number of neutrons and protons are approximately equal (N=Z).
Above bismuth the nuclides are all unstable to radioactive decay by a-particle emission, while some are also unstable to B-decay.
Low ratio
If the N/Z ratio is too low for stability, then radioactive decay occurs in such a manner as to lower Z and increase N by conversion of a proton to neutron.
This may be accomplished through:
Positron emission
Absorption by the nucleus of an orbital electron (electron capture, E.C).
High ratio
In such a case the nucleus must decrease the value of N and increase the value of Z, which can be done by conversion of a neutron to proton.
If a nucleus has a N/Z ratio too high for stability, it is said to be neutron-rich.
It will undergo radioactive decay in such a manner that the neutron to proton ratio decreases to approach more closely the stable value.
N/Z RATIO WITH HIGH Z
Stable nuclei- An attractive force hold the neutrons and protons together.
This attractive nuclear force must be sufficient in stable nuclei to overcome the Coulomb force.
Protons in the nucleus will experience a repulsive (destructive) Coulomb force.
As the number of protons increases, the total repulsive Coulomb force increases.
To provide sufficient attractive force for stability the number of neutrons increases more rapidly than that of the protons.