Binding Energy Formula

Binding Energy Formula

The binding energy is essentially the energy required to breakdown or separate a nucleus into its nucleons. Nucleons are protons, neutrons, and other nuclear particles that comprise an atom’s nucleus. The nucleons are kept together by forces known as the strong nuclear force. Similarly, the more tightly connected the nucleus components are, the greater the binding energy required to separate them. The Binding Energy Formula provided below can help you comprehend this better.

Usually, the binding energy is positive. It is thus because energy must be expended in pushing these nucleons, which are attracted to each other by the strong nuclear attraction, apart. Always remember that the mass of an atomic nucleus will be smaller than the total of the individual masses of the unbound component protons and neutrons, according to Einstein’s equation E=mc². This missing mass is referred to as a Mass Defect since it was discharged during the formation of the nucleus.

Formula of Binding Energy

The Binding Energy Formula is also known as BE and is connected to Einstein’s equation. It is written as E = mc²:

The energy needed to dismantle or separate a nucleus into its nucleons is known as the binding energy. Nucleons are the protons, neutrons, and other nuclear particles that make up the atom’s nucleus, as it can be seen, when talked about. The so-called strong nuclear force is a force that holds the nucleons together. Similar to this, the stronger the bonding energy needed to separate the components of the nucleus, the more tightly they are bound. The following Binding Energy Formula will aid students in better understanding this:

where the difference in mass following nucleus separation is referred to as a mass defect. Since Z is said to be the number of protons and N is said to be the number of neutrons, the mass of the nucleus must be equal to the sum of these two numbers, which is Zmp + Nmn. This sum less the total mass when the particles come together (mtot) is the resultant mass defect, and c is said to be the speed of light, with a value of c= 2.9979 x 108 m/s. The Binding Energy Formula is written as E = mc².

E = mc² is the Binding Energy Formula:

BE = (m) c² = [(Zm_p + Nm_n) – m_tot] c²

Usually, the binding energy is always in a positive number. It is so because one needs to spend energy in moving these nucleons, which are attracted 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. Experts refer to this missing mass as Mass Defect, which signifies that it was released when the nucleus was made. The Binding Energy Formula is written as E = mc².

Use of Binding Energy Formula

Nuclear physics uses the Binding Energy Formula to do calculations. It is most helpful in the two domains of nuclear fusion and nuclear fission. These two fields both focus on how light nuclei divide or fuse. In addition, it may be utilised to make a nuclear weapon and power.

Solved Examples

Question: Given that the mass of a beryllium-4 nucleus is 9.012182 u, what is its binding energy?

Answer: Calculating the mass defect of beryllium should be the initial step. This atom contains 5 neutrons and 4 protons. One proton has a mass of 1.00728 amu, and one neutron has a mass of 1.00867 amu:

[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.

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