Nuclear Binding Energy
In the nucleus of an atom, protons and neutrons (collectively known as nucleons) are held together by a strong, short-range attractive force called the nuclear force. This force is responsible for the stability of the nucleus.
To decompose a nucleus into its individual nucleons, energy must be supplied to overcome this attractive force. This required energy is known as nuclear binding energy.
What is Nuclear Binding Energy?
Nuclear binding energy is the amount of energy required to disassemble a nucleus into its individual protons and neutrons. It is also the energy released when a nucleus is formed from these nucleons.
Mass Defect and Binding Energy
One important observation in nuclear physics is that the total mass of a nucleus is always less than the sum of the individual masses of its protons and neutrons. This difference in mass is known as the mass defect (Δm). This “missing mass” has been converted into binding energy according to Einstein’s famous equation: E=Δmc2E = \Delta m c^2
Where:
- Δm\Delta m = mass defect
- cc = speed of light
Let:
- MpM_p = mass of one proton
- MnM_n = mass of one neutron
- ZZ = number of protons
- AA = mass number (total nucleons)
- N=A−ZN = A – Z = number of neutrons
- MNM_N = mass of the nucleus
Then the mass defect is: Δm=[ZMp+(A−Z)Mn]−MN\Delta m = [Z M_p + (A – Z) M_n] – M_N
And the nuclear binding energy becomes: EB=Δm⋅c2E_B = \Delta m \cdot c^2
Average Binding Energy
The average binding energy is the total nuclear binding energy divided by the number of nucleons (A): Average Binding Energy=EBA\text{Average Binding Energy} = \frac{E_B}{A}
It represents the average energy needed to remove a single nucleon from the nucleus.
Average Binding Energy Curve
The average binding energy curve is a graph that plots average binding energy per nucleon versus the mass number (A) of nuclei.
From this curve, we observe:
- The average binding energy is always positive, meaning energy is released during nucleus formation.
- Light nuclei like hydrogen (1H^1H, 2H^2H) have very small binding energies, making them suitable for nuclear fusion.
- Nuclei with equal numbers of protons and neutrons (like 4He^4He, 8Be^8Be) show peaks in the curve, indicating greater stability.
- For mass numbers between 20 and 180, the average binding energy remains almost constant (around 8.5 MeV), with iron-56 (56Fe^{56}Fe) having the maximum binding energy of about 8.8 MeV. These nuclei are the most stable.
- For heavy nuclei (A > 120), the average binding energy decreases due to increasing electrostatic repulsion between protons. For uranium, it’s about 7.6 MeV.
- Nuclei heavier than uranium become unstable and often radioactive, due to the overwhelming repulsion between too many protons.
Importance of Average Binding Energy
- It helps explain why fusion occurs in light elements (small average binding energy), and fission in heavy elements like uranium (which can split into more stable fragments).
- A higher average binding energy per nucleon means a more stable nucleus.
- The fact that binding energy is positive for all nuclei shows that energy is released during nuclear formation.
Define Nuclear Binding Energy
To define nuclear binding energy in simple terms:
It is the energy required to break a nucleus into its individual protons and neutrons, or the energy released when these nucleons come together to form a nucleus.
