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Useful Nuclear Physics Basics for Interested People

Mass-energy relation

albert einstein

Mass and energy are inter-convertible according to Einstein. That is mass and energy can be changed from one form to another. Thus mass is another form of energy. So, the energy produced by the conversion of a mass is E = mc2 where E is the energy in joules, m is the mass in kg, and c Is the velocity of light in a vacuum.

In nuclear interaction, conversion of mass into energy and vice versa takes place naturally, according to the above relation. This relation shows that even small particles like the nucleus have an enormous amount of energy.

According to Einstein, the energy equivalent of mass is given by E = mc2 where c=108m/s) is the speed of light in a vacuum. We know that 1 amu = 1.66 x 1027 kg, The energy equivalent of 1 amu = (1.67 x 1027) (3 x 108) = 931.3MeV.

Electron Volt

Electron volt(eV) is the energy gained by an electron when accelerated through a potential difference of one volt. 1eV = 1.67×10-19J.

Mass Defect (Δm)

It is found that the mass of a stable nucleus is always less than the sum of the masses of constituent protons and neutrons in their free state. The difference between the rest mass of the nucleus and the sum of the rest masses of constituent nucleons is called the mass defect.

Mass Defect Δm = (Zmp+(A-Z)mn) –  M.


Nuclear Binding energy

nuclear binding energy curve
Roderich Kahn/CC BY-SA 4.0

The nucleons inside the nucleus are held together by a strong nuclear force. A definite amount of energy is required to break the nucleus into constituent nucleons. The minimum amount of energy required to split the nucleus into its constituent nucleons is called the binding energy of the nucleus.

That is the energy that binds the nucleons to form a stable nucleus. The mass defect Am is equivalent to the binding energy. If ΔE is the energy released when neutrons and protons are brought together to form the nucleus then ΔE = Δmc2.

Binding energy per nucleon

The ratio of the binding energy of the nucleus to its mass number A is called binding energy per nucleon. Specific binding energy is the binding energy per nucleon. It is the average energy per nucleon needed to separate a nucleus into its individual nucleons. The Stability of the nucleus will be greater if specific binding energy is greater.

Binding energy curve

A graph of binding energy per nucleon drawn against the mass number is called a binding energy curve. That is, it is a graph of specific binding energy vs mass number A.

Models of Atom: Thomson, Rutherford, Bohr, Plum Pudding, Electromagnetic Rays, Experiment, Etc.

Facts about binding energy

The binding energy per nucleon is almost constant in the range of 8MeV. It is independent of A in the range 30<A <170 as they have the largest specific binding energy. The curve raises rapidly in the beginning and reaches a maximum of 8.75MeV for iron (A=56) and decreases to 7.6MeV for uranium (A=238).

The binding energy per nucleon for light nuclei is very small. For example, Li, He, etc. Nuclei heavier than U-238 has very small binding energy per nucleon so they are highly unstable and radioactive. A heavy nucleus has lower binding energy per nucleon.

If the nucleus breaks into two nuclei, the nucleons get more tightly bound. Energy would be released in fission since binding energy per nucleon increases. In fusion, two light nuclei combine to form a heavier nucleus.

The final system is more tightly bound than the initial system and energy would be released. In the region of small mass numbers, the curve shows maxima and minima characteristics. The nuclei containing an odd and equal number of protons and neutrons show minima. The nuclei containing an even, and an equal number of protons show maxima.

Nuclear force

nuclear force graph
Fedosin/CC BY-SA 3.0

The strong attractive force that binds the nucleons (protons and neutrons) together inside the tiny nucleus is called nuclear force.

Basic Concepts of Chemistry: Matter, Solid, Elements, SI Units, Significant Figures, Accuracy, Precision, Etc.

Facts about the nuclear force

The nuclear force is the Strongest force in nature. It is about 1038 times as strong as gravitational force. Nuclear forces are short-range forces. It operates in the range of 2 fm and is negligible beyond 4 fm. nuclear forces are charge independent.

Force between proton and proton and proton and neutron are almost the same. Nuclear force has the property of saturation. A nucleon interacts with only neighboring nucleons. The binding energy of the nucleus is proportional to the mass number (A).

Nuclear force has a repulsive core. For a distance less than 8fm, nuclear forces are repulsive. The nuclear force is spin-dependent. The nuclear force between two nucleons is due to the exchange of mesons between them. Nuclear forces are non-central forces. The force between the two nucleons does not act along the line joining their centers.

Nuclear Physics Basics: Nuclei, Atomic Mass Unit, Neutron, Isotopes, Isobars, Isotones, Size, Charge, Etc.

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