# Binding Energy Formula

## What is Binding Energy of Nucleus Formula?

The binding energy equation shows the energy equivalent to the mass defect. This is also termed binding energy. The nucleus is the collection of protons and neutrons, present inside the atom. As the protons are positively charged and neutrons are neutrally charged particles. The nucleus of an atom is a positively charged particle. The nucleus looks like an inflexible spherical ball moulded together with many miniature spherical balls in nucleon form. These nucleons require bounding particles to keep them collected. This material will act as glue. Every nucleon needs to donate some amount of its mass to deliver energy, which results in a mass defect.

The total binding energy formula defines the total energy required to break down a nucleus into its component nucleons. The values obtained from the nuclear binding energy formula are expressed in terms of kJ/mole or MeV’s/nucleon.

The values obtained from the binding energy per nucleon formula will vary from atom to atom. It depends on the strength of the nucleus present inside the atom.

### Total Binding Energy Formula

Binding Energy = mass defect * c$^{2}$

where c represents the speed of light in a vacuum. Which has the constant value.

c = 2.9979 x 10$^{8}$ m/s.

The mass defect formula can be denoted by Δm

Mass defect formula Δm is given below

Δm = [Z(m$_{p}$ + m$_{e}$) + (A – Z)m$_{n}$] – m$_{atom}$

Here

m$_{p}$ denotes the mass of a proton (1.007277 amu)

m$_{n}$ denotes the mass of a neutron (1.008665 amu)

m$_{e}$  denotes the mass of an electron (0.000548597 amu)

M$_{atom}$ represents the mass of the nuclide

Z represents the atomic number

The binding energy of electrons is also called the ionization potential of the atom. Which in terms, the energy required to remove an electron from an atom, or a molecule, or an ion. The binding energy of a single neutron or photon of the nucleus is much greater than the binding energy of electrons in an atom.  The value obtained from the binding energy of electron formula is in eV. The approximate value of 1eV = 1.6 x 10$^{-19}$.

The binding energy of the nucleus formula is to calculate the energy required to break a nucleus into the constituents of protons and neutrons. About two million electron volts are required to break a part of deuterons into protons and neutrons.  The binding energy of the nucleus formula can be calculated by converting the mass to energy by using Maxwell's equation E = mc$^{2}$. The mass can be obtained from the mass defect equation. The unit of mass should be kg. The value which is converted from mass to energy is measured by the joules for one nucleus. The joules of one nucleus can be used to calculate per-nucleon and per-mole quantities.

### Problems Based on Binding Energy

Problem 1: Find the binding energy per nucleon for an alpha particle whose mass defect is given as 0.0281amu.

Given: mass defect = 0.0281amu

The formula of mass defect to convert into kg (1 amu = 1.6606 x 10$^{-27}$ kg)

Mass defect  =(0.0281)(1.6606 x 10$^{-27}$)= 0.04666 x 10$^{-27}$ kg/nucleus

For converting into energy using ΔE = Δmc$^{2}$,

where c = 2.9979 x 10$^{8}$ m/s.

E = (0.04666 x 10$^{-27}$)(2.9979 x 10$^{8}$ )$^{2}$ = 0.419377 x 10$^{-11}$ J/nucleus

For converting energy from J/nucleus to kJ/mole

(1 kJ = 1000 J)

To convert nucleus to mole by multiplying with the Avogadro number (6.022 x 10$^{23}$ nuclei/mol)

Therefore, E = (0.419377 x 10$^{-11}$)(6.022 x 10$^{23}$)/1000

Binding Energy E = 2.5254  x 10$^{9}$ kJ/mole