 # Binding Energy Formula

The binding energy is basically the energy which one requires to disassemble or separate a nucleus into its nucleons. When we talk about nucleons, we see that they are protons and neutrons plus other nuclear particles which make up the nucleus of an atom. The nucleons are held together through forces which we refer to as the strong nuclear force. Similarly, the higher the nucleus components are bound, the greater will be the binding energy which it requires in order to separate them. Binding Energy Formula given below will help you understand this better.

Usually, the binding energy is always in a positive number. It is so because one needs to spend energy in moving these nucleons which attract to each other by the strong nuclear force, away from each other. Always remember that the mass of an atomic nucleus will be lesser than the sum of the individual masses of the free constituent protons and neutrons, as per the equation by Einstein of E=mc2. We refer to this missing mass as Mass Defect, which signifies that was released when the nucleus was made.

### Binding Energy Formula

One can also refer to Binding Energy as BE and is related to the equation by Einstein which is E = mc2:

BE = (m) c2 = [(Zmp + Nmn) – mtot] c2

Where is referred to as mass defect and it is the difference of the mass after the nucleus separates. As Z is said to be the number of protons and N is the number of neutrons, the nucleus mass must be the sum of both of these which is Zmp + Nmn then, this sum minus the total mass when the particles come together (mtot) is the resultant mass defect and c is referred to be the speed of light having the value c= 2.9979 x 108 m/s.

### Use

We use binding energy in order to calculate in the field of nuclear physics. It is essentially useful in two fields we well, which are nuclear fusion and nuclear fission. Both of these areas study the light nuclei fuse or nuclei split. Moreover, it is used to produce electricity as well as a nuclear weapon.

### Solved Example for You:

Question- Find out the binding energy of a beryllium-4 nucleus, the mass of the nucleus is 9.012182 u.

Answer- Your first step should be to calculate the mass defect of beryllium. This atom has 4 protons and 5 neutrons. Over here, the mass of 1 proton is 1.00728 amu and mass of each neutron is 1.00867 amu/ neutron:

[4 protons (1.00728 u) + 5 neutrons (1.00867 u)] – 9.012182 u = 0.060288 u × 1.6606 × 10-27 kg/amu = 1.00114 × 10-28 kg/nucleus

Thus, the binding energy is BE = (m) c2 = 0.060288 u (2.9979 × 108 m/s) 2 = 8.9976 × 10-12 J/nucleus.

#### Considerations

The units are said to be the units of energy which is Joules or eV per nucleus. It is important to notice that the total mass of a nucleus when the nucleons are together is smaller when we compare it to the total of the particles separated. It is invariable for all the atoms.

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