# What is Nuclear Mass Defect? What is Nuclear Binding Energy?

Mass Defect: The total number of protons and neutron is known as nucleons. The difference between the mass of a nucleus and the sum of the masses of the nucleons of which it is composed is called the mass defect.  When the nucleus formed by nucleons than it is find that the expected mass of nucleus is grater than the sum of the masses of the nucleons. The difference of the masses is known as Mass Defect.

Mass Defect = [Number of Protons X Mass of a proton + Number of Neutron

X Mass of Neutron] – Actual mass of Nucleus

The symbolization of an atom is represented as   than

Mass Defect =>  Δm = [Z X mp+ (A-Z) mn]-M

where: Δm=mass defect (amu); M = Actual mass of Nucleus (Atomic Mass) mp=mass of a proton   (1.007277 amu); mn=mass of a neutron (1.008665 amu); me=mass of an electron   (0.000548597 amu)

 Particle Mass (kg) Mass (u) Mass (Mev/c2) 1 atomic mass unit 1.660540 x 10-27 kg 1.000 u 931.5 MeV/c2 neutron 1.674929 x 10-27 kg 1.008664 u 939.57 MeV/c2 proton 1.672623 x 10-27 kg 1.007276 u 938.28 MeV/c2 electron 9.109390 x 10-31 kg 0.00054858 u 0.511 MeV/c2  For carbon-12 atom as   :

The carbon-12 atom has a mass of 12.000 u, and yet it contains 12 objects (6 protons and 6 neutrons) that each has a mass greater than 1.000 u:

Mass defect => Δm = 6 X 1.008664 u + 6 X 1.007276 u + 6 X 0.00054858 u – 12.000 u = 0.098931 u

The binding energy in the carbon-12 atom is therefore 0.098931 u X 931.5 MeV/u = 92.15 MeV.

Once mass defect is known, nuclear binding energy can be calculated by converting that mass to energy by using E=mC2.

Binding Energy: The Nuclear binding energy is equal to the energy librated when nucleus is formed from other nuclei. Every nuclei has some binding energy which is depends upon the number of nucleons of nucleus. If mass number is 20<A<200; then per nucleon binding energy is ~8.0 Mev and these types of nucleus is in stable state. For those nucleus having A>200; than per nucleon binding energy is about ~7.6 Mev and nucleus are unstable.

Binding Energy B = (Δm).C2

B = [{Z X mp+ (A-Z) mn}-M]. C2

The nuclear binding energy may also refer to the energy balance in processes in which the nucleus splits into fragments composed of more than one nucleon. If new binding energy is available when light nuclei fuse, or when heavy nuclei split, either process can result in release of this binding energy. When a large nucleus splits into pieces, excess energy is emitted as photons (gamma rays) and as the kinetic energy of a number of different ejected particles (nuclear fission products). The nuclear binding energies and forces are on the order of a million times greater than the electron binding energies of light atoms like hydrogen. The mass defect of a nucleus represents the mass of the energy of binding of the nucleus, and is the difference between the mass of a nucleus and the sum of the masses of the nucleons of which it is composed.

For the alpha particle Δm= 0.0304 u which gives a binding energy of 28.3 MeV.

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