Binding Energy

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What is Binding Energy?

Everything we see around has some binding force and the energy by which they are bound is the binding energy. A nucleus has electrons and protons and they are tightly bound by the energy and the smallest energy required to remove an electron/proton/neutron from the nucleus is the binding energy.

For instance, a system is made up of many subatomic particles and for removing a single particle, we need the smallest magnitude of energy and that energy is the binding energy. 

In this article, we’ll understand the binding energy definition, binding energy formula, and do the binding energy curve explanation.

Binding Energy Definition

In Physics, the concept of binding energy is employed in condensed matter physics, atomic physics. In Physics, the binding energy is used to take away or rearrange particles from the system of particles.

Binding Energy Examples

You can consider the concept of rotational dynamics. A body rotating about its axis contains millions of particles rotating with itself. Here, if we wish to separate a particular particle from the system of particles, we need the energy called the binding energy. 

Another example, millions of electrons are circulating inside the wire, now, if you wish to pull one electron from a big stream of electrons, you may need a smaller amount of energy. The energy you might need here is the binding energy.

Binding Energy in Nuclear Physics

In terms of Chemistry, Binding energy is the amount of energy required to separate or disassemble subatomic particles in atomic nuclei, like removing or rearranging electrons bound to nuclei in atoms, and atoms and ions tightly bound together in crystals.

So, Do You Know What is Binding Energy in Nuclear Physics?

Nuclear Physics word clearly signifies that we are talking about the science behind removing or disassembling subatomic particles from their parent home, i.e., nucleus. The energy required here is the Binding Energy. 

So, here, when we use the energy to separate an atomic nucleus into its constituent protons and neutrons is the Nuclear Binding Energy

Now, if we wish to combine these individual protons and neutrons into an atomic nucleus, some energy is liberated from their combination.

We measure the binding energy of separation in KJ/mol. Where the binding energy of hydrogen nucleus is 2.23 MeV or Mega electronVolt.

Binding Energy Curve Explanation

We know that the mass of a nucleus is lesser than that of the sum of its constituent protons and neutrons. Now, if we take a glimpse at the same number of protons and neutrons as in the nucleus we were trying to recreate, we find that the total mass of the individual protons and neutrons is always greater than when they are arranged as an individual nucleus. 

The difference in the mass between the sum of the products and the sum of the individual nucleons is known as the mass defect. The definition of binding energy per nucleon is the amount of energy required to break the nucleus into protons and neutrons again; the larger the binding energy, the more difficult it would be to separate subatomic particles from their nucleus. The figure below shows the binding energy for each element, against their atomic number (Z):

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Starting from H2, as we increase the atomic number, the binding energy also increases. So He has a greater binding energy per nucleon than the binding energy of hydrogen while Li has greater binding energy (in KJ/mol) than Helium, and Beryllium has greater binding energy than Lithium, and so on. We observe that this trend continues till we reach iron. After that, it begins to decrease slowly.

Binding Energy Curve

We can obtain the binding energy by dividing the total nuclear binding energy by the number of nucleons. We find that there is a peak in the binding energy curve in the region of stability in iron, which means that either the breakup of heavier nuclei aka fission or the combining of lighter nuclei aka fusion will produce nuclei that are more tightly bound; however, they bear less mass per nucleon.

Nuclear Binding Energy Curve Explanation

When the individual protons and neutrons combine to form a nucleus again, the mass that disappears is the mass defect, abbreviated as ∆m) gets converted into an equivalent amount of energy Δmc2 ; this energy is the binding energy of the nucleus.

Here, Δmc2 is the Binding Energy Formula, also called the Einstein Energy-Mass Equation.

Mass change or Δm = (calculated mass of the unbound system) − (measured mass of the system)

For example, in the case of nuclear physics, the formula becomes:

Δm = sum of masses of protons and neutrons − the measured mass of a nucleus

c = 3 x 108 m/s .

Do You Know?

The binding energy is directly linked with fusion and fission. The lighter elements up to Iron release energy through the fusion process, while in the opposite direction the heaviest elements below Iron are more susceptible to liberate energy through fission.

FAQ (Frequently Asked Questions)

1.  State Two Types of Binding Energy.

Ans: The two types are as follows:

1. Electron binding energy

Electron binding energy or ionization energy is the energy that we need to free an electron from its atomic orbital. The electron binding energy is derived from the electromagnetic interaction of the electron with its nucleus and the other electrons of the atom/ molecule and is intervened by photons.

2. Bond dissociation energy

Bond dissociation energy is the measure of the binding energy between the atoms in a chemical bond. It is the energy required to re-localize a molecule into its constituent atoms. This energy appears as chemical energy, like that released in chemical explosions, the burning of chemical fuel, and biological processes. A bond generally in the range of a few eV per bond.

2: Determine the Binding Energy/Nucleon For an Alpha Particle Whose Δm is 0.029 amu.

Ans: We are given with mass defect = 0.029 amu

We know that 1 amu = 1.6606 x 10 -27 kg

So, Mass defect in kg  = (0.029)* (1.6606 x 10-27) = 0.04848 x 10-27 kg/nucleus

Now, using the energy-mass equation:

ΔE = Δmc2

Putting c = 3 x 108 m/s

E = (0.0482 x 10-27)(3 x 108)2  = 0.433 x 10-11 J/nucleus

We know that the Binding Energy is always in  kJ/mole and 1 J = 1/1000 KJ

Now, multiplying with the Avogadro number 6.022 x 1023 nuclei/mol.

Therefore, E = (0.433 x 10-11) (6.022 x 1023)/1000

Binding Energy E = 2.607  x 109 kJ/mole