MASS ENERGY AND NUCLEAR BINDING ENERGY

MASS DEFECT/BINDING ENERGY

The difference between the sum of the masses of nucleons ( protons and neutrons) in the nucleus and the actual mass of the nucleus is called mass defect. Now the question is where did the reduced mass go?

During the formation of the nucleus, this reduced mass is loosed in the form of energy. And according to Einstein mass-energy equivalence relation, This energy will be

\fn_cm \large E_b=\Delta m c^2

where \fn_cm \large \Delta m\rightarrow mass defect

\fn_cm \large c\rightarrow speed of light

This energy is called the Binding Energy of the nucleus.

” In other words, if we separate a nucleus into its nucleon, we would have to supply total energy equal to \fn_cm \large E_b , to that particle.”

BINDING ENERGY PER NUCLEON OF A NUCLEUS

The Binding energy per nucleon is the average energy required to extract one nucleon from the nucleus to ∞ distance.

i.e  \fn_cm \large E_{bn}(B.E/ nucleon)= \frac{Total \;B.E(E_b)}{Mass \;No(A)}

The stability of the nucleus is determined by binding energy per nucleon.

The greater the binding energy per nucleon, the more stable is the nucleus and vice versa.

From the fig,

  1. The binding energy per nucleon is practically constant i.e \fn_cm \large E_{bn} is independent of the atomic number for nuclei of middle mass number (30<A<170)
  2. \fn_cm \large E_{bn} has a maximum of about 8.75 Mev for A=56 and has a value of 7.6 Mev for A=238.
  3. \fn_cm \large E_{bn} is lower for both light nuclei (A<30) and heavy nuclei (A>170)

Some conclusion from these observations:-

  1. The force is attractive and sufficiently strong to produce binding energy of a few MeV per nucleon.
  2. A very heavy nucleus, say A = 240, has lower binding energy per nucleon compared to that of a nucleus with A = 120. Thus if a nucleus A = 240 breaks into two A = 120 nuclei, nucleons get more tightly bound. This implies energy would be released in the process. It has very important implications for energy production through fission.
  3. Consider two very light nuclei (A ≤ 10) joining to form a heavier nucleus. The binding energy per nucleon of the fused heavier nuclei is more than the binding energy per nucleon of the lighter nuclei. This means that the final system is more tightly bound than the initial system. Again energy would be released in such a process of fusion. This is the energy source of the sun.

NOTE:

binding energy is not the criteria for checking the stability of the nucleus

B.E of Heavy Hydrogen= 2.23 MeV

B.E of Uranium= 1800 MeV

Both elements participate in the radioactive rection but their binding energy is different.

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